FIL COPY

0

.DT

COMPARING RANKING HEURISTICS FOR THEPRODUCTIVITY INVESTMENT FUND PROGRAM:

A CAPITAL RATIONING PROBLEM

THESIS

Albert F. SpalaCaptain, USAF

AFIT/GSM/LSY/89D-38

App.: ~ :~ireleasel

DEPARTMENT OF THE AIR FORCE

AIR UNIVERSITY

AIR FORCE INSTITUTE OF TECHNOLOGY

Wright-Patterson Air Force Base, Ohio

90 OF2 2 00 9

AFIT/GSM/LSY/89D-38

DTIC

ELECTE

~D

COMPARING RANKING HEURISTICS FOR THEPRODUCTIVITY INVESTMENT FUND PROGRAM:

A CAPITAL RATIONING PROBLEM

THESIS

Albert F. SpalaCaptain, USAF

AFIT/GSM/LSY/89D-38

Approved for public release; distribution unlimited

The contents of the document are technically accurate, and nosensitive items, detrimental ideas, or deleterious information iscontained therein. Furthermore, the views expressed in thedocument are those of the author and do not necessarily reflectthe views of the School of Systems and Logistics, the AirUniversity, the United States Air Force, or the Department ofDefense.

Accesion For

NTIS CRA&DTIC TAB 0]Un annol , ic.ed L

ByDistr ibt, tion I

Availbiihty CodesAVdII ,dlor

Dist special

AFIT/GSM/LSY/89D-38

COMPARING RANKING HEURISTICS FOR THE

PRODUCTIVITY INVESTMENT FUND PROGRAM:

A CAPITAL RATIONING PROBLEM

THESIS

Presented to the Faculty of the School of Systems and Logistics

of the Air Force Institute of Technology

Air University

In Partial Fulfillment of the

Requirements for the Degree of

Master of Science in Systems Management

Albert F. Spala, B.S.

Captain, USAF

December 1989

Approved for public release; distribution unlimited

AcknowledgAements

This study would not have been accomplished without the

help and support of many individuals to whom I am eternally

grateful. Capt David S. Christensen's study provided the

starting point for this thesis. I am also grateful to Capt

Christensen for being my advisor for this thesis and guiding

my efforts with skill, patience, and understanding.

I also want to express my extreme thanks to Lt Col

Phillip E. Miller for his guidance and support outside the

classroom that was above and beyond the call of duty.

Thanks also to all of my fellow students and AFIT faculty

members who more than once sacrificed of themselves for me.

But most of all, I wish to express my love and thanks

to my wife Tina, and sons David and Matthew. Without Tina's

help, love, and extreme patience this study could not have

been completed. A special thank you to my sons for

continuing to love me, despite the many times Daddy was too

busy for you.

Finally, I wish to thank the United States Air Force

and the Air Force Institute of Technology for giving me the

opportunity to complete my graduate studies.

Albert F. Spala

ii

TAble nf Contents

Page

Acknowledgements. ...................... ii

List of Figures. ...................... v

List of Tables. ....................... vi

Abstract .. ....................... vii

I. Introduction .. .................... 1

General Issue. .................. 1Statement of the Problem .. ............ 3Research Hypothesis. ............... 4Scope of the Research .. ............ 4Limitations of the Study .. ............ 5Assumptions. ................... 6Summary. ..................... 6

ii. Literature Review. .................. 8

Ranking and Economic Criteria ...... 9Simulation as a Tool. .. ............ 11Summary ...................... 17

III. Methodology ...................... 20

Selection of the Model. .. ........... 20Research Design .................. 21Overview of the QUATTRO Simulation Model. 27Development of the Simulation Model . . .29The QUATTRO Simulation. .. ........... 33The Random Number Generator. ........... 33Data Generation .................. 37Ranking Criteria and NPV Calculation .. . 43Project Fanking .. ............... 45Project Selection (The DoD Method) .. . . 47Project Selection (The Carry-Over Method) 49Net Present Value Calculations .. ......... 49Hypothesis Testing. .. ............. 50Sensitivity Analysis. .. ............ 51Summary ...................... 52

IV. Findings and Discussion......... .. .. .. .... 53

Normality Testing .. .............. 56Paired Sample T Test. .. ............ 57Hypothesis Rejected .. .............. 6Sensitivity Analysis. .. ............ 60Discussion. .................... 63Summary ...................... 64

iii

Page

V. Conclusions and Recommendations. ........... 66

Summary ...................... 66Conclusions .. .......................... 66Recommendations for Further Research . . . 67

Appendix A: Sample Template Entries by CellLocation .................... 69

Aplpendix B: Sample Simulation Output. ........... 78

Appendix C: Annual Net Present Value Results ... 85

Bibliography .. ................. ........ 91

Vita. ........................... 93

iv

List of Figures

Figure Page

1. Simplified Research Design Flow Chart ..... 22

2. Simulation Logic Flow Chart .. .......... .. 30

3. Simulation Process Block Diagram .......... .. 34

4. Normality Plot of the Results .. ......... .. 58

V

List of Tables

Table Page

1. The Most and Least Popular EvaluationMethods ........... .................... 10

2. Results Achieved through Five Cycles ofSimulation ...... .................. .. 16

3. Results of Whitaker Study ....... ........... 18

4. FY85 PIF Program Summary Statistics ...... .. 24

5. Summary Statistic Comparison .......... .. 28

6. Annual PIF Program Budget Ceilings ...... 32

7. Random Number Generator Starting Points . . .. 36

8. Five Year NPV Total Results of theSimulation .. .......... ................. 54

9. Descriptive Statistics of Simulation Results(Five Year NPV Totals) ... ............ .. 55

10. Critical t Values for the t Distribution . . 59

11. Five Year NPV Totals Using EPI as the SoleRanking Criterion .... ............... ... 61

12. Descriptive Statistics of Simulation ResultsUsing EPI as the Ranking Criterion .... ...... 62

13. Descriptive Statistics of Simulation Results(Comparison of DoD and EPI Ranking Criteria) 62

vi

AFIT/GSM/LSY/89D-38

The purpose of this study was to compare two capital

rationing heuristics as they apply to the Department of

Defense (DaD. Productivity Investment Fund (PIF) program.

Specifically, it addressed the research question: Is the

net present value (NPV) of capital investment projects

selected using the current DoD method less than-the NPV of

projects selected using an alternative Carry-over method of

project selection?

The current DoD method of project selection allows the

skipping of economically attractive projects to maximize the

use of an annual budget. The alternative Carry-over method

would not allow skipping and would carry the funds remaining

to the next annual budget without penalty. The larger

budget in the subsequent year could allow the funding of a

more economically attractive project that might otherwise be

skipped. The result may be more long term economic savings

to the DoD.

The study was performed using a QUATTRO personal

computer spreadsheet simulation. Project characteristics

were generated based on FY85 PIF data and the process of

project selection was performed over a five year period.

Annual budgets were kept constant at $150 million (M) except

for the funds remaining from the previous years. -

The study found that the five year total NPV of projects

selected using the current DoD method was dreater than the

vii

alternative Carry-over method by an average of $5.135 M.

However, sensitivity analysis showed that by using excess

profitability index (EPI) as the only ranking criterion, the

five year NPV total of projects selected using the DoD

method of skipping could be inased by $63 M. The NPV of

projects selected using the Carry-over method and the EPI

criterion also i by an average of $64 M. The DoD

method using the EPI criterion was still guoprinr to the

Carry-over method by an average of $4.234 M.

viii

COMPARING RANKING HEURISTICS FOR THE

PRODUCTIVITY INVESTMENT FUND PROGRAM:

A CAPITAL RATIONING PROBLEM

I. Introduction

General Issue

The Productivity Investment Fund (PIF) program is a

subset of the Department of Defense (DoD) Productivity

Enhancing Capital Investment (PECI) program that involves

capital rationing. Capital rationing is a subset of capital

budgeting where funds for financing long-term investment

projects are limited by one or more budget ceilings (1:1).

The capital budgeting process can be divided into several

distinct steps. These steps are identified by Quirin as

project generation, project evaluation, project selection,

and project execution (10:15). This study focuses primarily

on the capital rationing problem with regard to project

selection in the PIF program.

Generally, the objective of the PECI program is to

achieve more economically efficient defense organizations

through productivity enhancing capital investments. These

investments, or PECI projects, are typically improvements in

existing facilities or acquisitions of new equipment which

improve methods of operation. Primary emphasis is on

realizing savings through the substitution of capital for

-- -=,= -- -- m an nn~u~m I IINIB HIR R H 1

labor, thereby reallocating saved personnel spaces. PIF

projects are PECI projects which meet the criteria estab-

lished by regulation of an initial investment cost of at

least $100,000 and an amortization, or payback, period of

four years or less (2:4).

PIF projects are submitted annually by ell DoD com-

ponents and compete for funding from a limited capital bud-

get. Yearly submittals from FY82-FY86 ranged from 86 to 198

projects. The total investment costs ranged from $279

million (M) to $528M. Budget ceilings ranged from $90M to

$139M (1:15).

The DoD currently employs a ranking method for project

selection. Projects are evaluated and assigned rankings

based on three separate economic indicators. These indica-

tors are internal rate of return (IRR), return on investment

(ROI), and cost per manpower space saved (CPM).

Each project is assigned a rank based on each indicator

separately. These rankings are then totalled for an overall

rank. Projects then compete for funding based on their

overall rank. Projects are selected for funding until the

first project is reached with a cost that exceeds the funds

remaining in the budget. This project is skipped and the

next lower ranked project is considered. If possible, this

project is funded; otherwise it is skipped and the next

project is considered. This process continues until the

funds are exhausted or are insufficient for any remaining

project.

2

The process of skipping economically attractive pro-

jects in favor of less attractive projects, because of the

funding constraint, may result in less savings than could

be realized by carrying over the funds remaining to the

following year. By carrying the funds over to the next

year, a larger budget would be realized which may result in

the ability to fund more economically attractive projects.

This may result in even more efficient defense organizations

downstream.

The process of maximizing the use of a given budget is

a well-known phenomenon in the government. Organizations

are penalized by either underspending or overspending their

allocated funds (16:301). Although perhaps not a good

analogy, are government budgets better utilized by buying a

three-year supply of pencils to avoid being penalized in the

next year's budget, or by carrying the money over without

penalty? This type of question suggests the importance of

exploring the effect of skipping economically attractive

projects in order to use all available funds.

Statement of the Problem

The purpose of this study is to compare two capital

rationing heuristics as they apply to the PIF program.

Specifically, is the net present value (NPV) of projects

selected by the current DoD method less than the NPV

realized by a Carry-over method. The Carry-over method

would cease project selection when the first project is

reached whose investment cost exceeds the funds remaining.

3

These remaining funds would be carried over to the next

fiscal year budget. The question above will be addressed by

a personal computer spreadsheet simulation. The model will

generate project characteristics and projects will be

selected according to each method described above and the

NPV's of the portfolios selected by each method will be

compared.

Research Hypothesis

The research hypothesis for this study is as follows:

The NPV of projects selected for the PIF program by the

Carry-over method is greater than the NPV of projects

selected by the current method employed by the DoD (which

allows the skipping of projects until the funds are

exhausted). NPV is the difference between the sum of the

discounted cash inflows (savings realized by implementation

of the project) and the sum of the discounted cash outflows

(initial investment cost plus any additional yearly costs).

The null hypothesis for this study is:

Ho: The NPV of the Carry-over method - NPV of theDoD method = 0.

HA: The NPV of the Carry-over method - NPV of theDoD method > 0.

HA: The NPV of the Carry-over method - NPV of theDoD method < 0.

Scope of the Research

This study will utilize existing data of PIF projects

for FY85 as presented by Christensen (1). The data will be

4

evaluated to determine the summary statistics for various

project characteristics which will be used to generate

simulated projects. The main characteristics of interest

are cash flow patterns and project life. A computer

simulation model will be developed to simulate the PIF

project characteristics and selection process. The model

will allow the selection of projects according to each

method from an identical set of projects. This will allow

for the direct comparison of the NPV's of each method.

Limitations of the Study

As mentioned previously, many different economic

criteria are used in the area of capital budgeting for the

ranking and selection of capital investment projects. The

intent of this study is not to compare various economic

criteria to determine which would result in the optimal set

of investment projects. The intent is to compare two

heuristics using the same economic criteria that are

currently used by the DoD for the selection of PIF projects.

Also, the intent of this study is to compare these

techniques specifically as they apply to the PIF program.

Therefore, the project characteristics will be limited to

those which meet the specific eligibility criteria of a

minimum investment cost of $100,000, and a payback period of

at most four years. Based on the limitations of time and

data availability, project charateristics will be limited to

the characteristics of projects identified for FY85.

5

Assumot ions

Two major assumptions are made in this study. First,

the author assumes the ability to carry over funds from one

year to the next is a feasible alternative for consideration

in the method of project selection. Second, the author

assumes the project characteristics of FY85 PIF projects are

representative of all yearly project submittals.

This chapter has briefly described the objective of the

PIF program and the current ranking method used by the DoD

to select projects which compete for funding from a limited

budget. The current method may result in less economically

efficient defense organizations than could be realized if an

alternative method were used. The alternative method would

allow for the carry-over of the funds that are left when the

first project is reached whose cost exceeds that amount.

This would result in larger subsequent yearly budgets which

may result in larger long-run savings to the DoD.

This study is relevant because although ranking may not

result in an optimal economic mix of projects, it is a

popular approach among many businesses (4:301). However, it

is still desirable to find the best economic mix of projects

for increased future savings. An alternative use of the

ranking method may provide a better economic mix of pro-

jects; resulting in greater savings to the DoD.

6

The next chapter provides a review of the literature

relevant to the PIF program and the role of simulation as a

tool in the area of capital budgeting.

7

II. Literature Review

An extensive study of the PIF program was conducted by

Christensen (1). Christensen applied mathematical program-

ming (MP) to FY85 PIF data to demonstrate that the current

method of selecting projects used by the DoD results in a

suboptimal economic mix of capital investment projects.

Christensen concluded that "the use of MP to select PIF

projects will result in substantial dollar savings to the

DoD" (1:125). However, the DoD continues to use ranking as

the method of project selection.

As mentioned earlier, the method of skipping economi-

cally attractive projects to fully utilize the allocated

budget is typical of a well-known phenomenon in the govern-

ment. The following excerpt from an article by Zimmerman

illustrates why fully utilizing the budget is so common in

the government:

In fact, the sponsor may view any unspent currentfunds as indicating surplus in the agency and mayreduce the agency's future budgets by, say, theamount of the unspent funds. On the other hand,there are strong sanctions which impose costs onan agency if its fiscal spending limit is exceeded.The sponsor may initiate a general audit in responseto a budget overrun, future budgets may be placedin jeopardy, and the "public's confidence" in theagency's managerial ability may be eroded. All ofthese perceived sanctions tend to focus the agency'smanagement on the efficacy of the fiscal budgetconstraint; management has incentives to "zero out"the budget at the end of the year. (16:301-302)

8

"However, if the DoD could hold large amounts of money over

to future years without penalty, increased savings may be

possible" (1:127). This idea is the focus of this study.

Ranking and Economic Criteria

Although ranking can result in a suboptimal economic

choice of capital investments, it is easy to apply and is

widely used in private and public sectors (6). The economic

criteria used to rank projects have been an area of interest

for many years, and have received considerable attention in

academic literature. "Criteria frequently analyzed include

net present value (NPV), annual worth, benefit-cost ratio,

internal rate of return (IRR), and payback" (15:7). Net

present value is accepted as the best criterion from a

theoretical standpoint and IRR as the second best (6:23).

However, a survey conducted by Kim and Farragher in 1979

revealed that a majority of large companies used IRR as the

main criterion for project selection (7:28). Also, another

survey was conducted of non-industrial firms which revealed

that "67 percent of the firms responding used IRR as the

primary evaluation technique" (4:299). In both cases NPV

was the second most preferred evaluation technique. This

illustrates an apparent conflict between theory and practice.

To further illustrate the interest in capital budgeting

practices of business firms, Scott and Petty presented a

summary of several surveys which were performed to determine

the evaluation methods of several businesses (10). Table 1

indicates the most-favored and least-favored evaluation

9

Table 1

The Most and Least Popular Evaluation Methods

Year Most LeastPublished Popular Popular Reference

1960 ppa DCFb Miller (13)1961 ARR DCF and MAPI Istvan (7)

formula1970 IRR NPV and PI Mao (1211970 IRR PI Williams (2111972 DCF PP, PP Klammer (10)

reciprocaland urgency

1973 IRR PI Fremgen (5)1975 IRR PI Brigham {1)1975 IRR NPVc Petty (1611975 IRR PI Petty, Scott,

Bird (17)1977 IRR PI Gitman and

Forrester (6)1978 PP NPVc Schall, Sundem,

Geijsbeek (19i

aThe abreviations used are as follows: PP is payback period,

DCF is discounted cash flow techniques, ARR is average rate ofreturn, IRR is internal rate of return, NPV is net presentvalue, PI is profitability index.

bWhen DCF is used in this table, the survey did not

distinguish among the various time-adjusted evaluation methods.

cThe PI was not identified as a possible response in the

questionnaire format.(11:115)

10

methods as indicated by the various surveys collected by

Scott and Petty. It can be concluded from all of the above

surveys that although many methods have been developed to

optimize the economic benefits from capital investments,

such as operations research techniques and mathematical

programming, the use of ranking is still the preferred

method of project selection in use by most businesses.

Simulation as a Tool

Simulation has been used to evaluate and compare capital

budgeting techniques. Primary emphasis has been on the

comparison of different economic criteria applied to identi-

cal project sets to evaluate which criteria would result in

greater profits or savings to a business enterprise. Most

of the literature comparing economic criteria evaluates them

as they would apply to one given set of projects at one

point in time. For example, Sundem used simulation to com-

pare a "NPV criterion with a payback constraint and a NPV

model with the discount rate dependent on the proposed

project's risk" (13:207). Sundem's model compared the

criteria as they applied to a given set of thirty projects

representing a variety of sizes, lives, and patterns of cash

flows (13:212). Sundem showed that:

(1) there is little synergistic effect of combininga net present value objective function with a paybackconstraint and (2) there is a possibility to increasegreatly the performance of a net present value modelby assigning projects to two or three risk classesand using a different discount rate for evaluatingprojects in each risk class. (13:226-227)

11

It is envisioned that the difference between the methods

of selection for the PIF program compared in this study

would be most apparent when evaluated over a period of

years. Three simulation studies which utilize comparisons

over time are significant for this study.

Para-Vasquez and Oakford described in general terms a

simulation of a hypothetical firm to compare capital budget-

ing decision procedures (9:221). The simulation was used to

compare the effectivenss of:

1. Sequential versus batch decision procedures.

2. Logically exact versus approximate selectionalgorithms in the batch decision procedure.

3. Three different decision procedures when themarginal growth rate of the firm cannot be estimatedaccurately. (9:225)

These procedures were compared over an eight year period.

In the sequential decision procedure, decisions were

made to accept/not accept projects individually as they

became available for consideration (9:226). In the batch

decision procedure, decisions were made annually on a given

set of available projects. Some variations of these pro-

cedures were also examined.

The authors concluded the firm would realize greater

capital growth by deciding on batches of proposals as

opposed to deciding on individual proposals as they became

available (9:227). In the case of the logically exact

versus approximate selection algorithm, the comparison was

very much like that performed by Christensen for the PIF

program (1). The approximate procedure used by the authors

12

was based on three independent rankings using three dif-

ferent ranking criteria (9:227). The proposals were ranked

according to each index separately and projects were

selected in sequence based on their ranking until funds were

exhausted. Skipping was allowed to maximize the utilization

of funds. This process was completed separately for each

criteria and a total Prospective Present Value (PPV) calcu-

lated for each combination of projects. PPV is similar to

NPV except it assumes that any cash left on hand when the

decision is made will be invested for one period at a

certain rate. If that rate is equal to the marginal growth

rate of the firm, then PPV and NPV are equal (9:232). An

extensive definition can be found in Para-Vasquez and

Oakford (9:232). The one with the highest PPV was chosen

and reported as a solution for the appropriate algorithm.

An exact mixed integer programming procedure basedon the algorithm for integer 0-1 programming byGeoffrion was developed for the solution of thelinear 0-1 mixed programming formulation of thecapital budgeting problems encountered by the hypo-thetical firm. (9:228)

The authors conducted this simulation for different

numbers of proposals (averaging 3, 6 and 12) per year over

an eight year period. They concluded that:

the use of well reasoned approximate selectionalgorithms may well be justified in firms that dealwith large numbers of proposals at each decisiontime. (9:229)

This is the case with the PIF program.

In the case of comparing three different decision

procedures when the marginal growth rate of the firm cannot

13

be estimated accurately, the decision criteria compared

were:

a. Approximate MPV (maximum prospective presentvalue) Criterion, using Prospective Present Valueas a measure of worth and the approximate selectionprocedure described above.

b. Approximate Net Present Value Criterion, usingNet Present Value as a measure of worth and theapproximate selection procedure described above.

c. Rank on PGR (prospective growth rate) withcutoff at the Marginal Growth Rate (MGR). The PGRis the only ranking index and the selection procedureis the approximate one described above. (9:230)

An extensive definition of MPV can be found in Para-

Vasquez and Oakford (9:232). PGR is identified by Para-

Vasquez and Oakford as being the same as internal rate of

return. The authors concluded that the three procedures

above are almost equally effective if the marginal growth

rate can be accurately estimated (9:231). If not, the

authors recommend using either PPV or PGR as the ranking

criterion.

White used computer simulation to compare investment

ranking criteria (15). White applied ten different economic

criteria to the same set of projects over a nine-year period

to compare the results of the net present value and rate of

return of the projects selected according to each criteria.

White used project lives of two and ten years which were

randomly generated following a uniform distribution (15:29).

The cash flow pattern of the projects was arbitrarily set as

a positive uniform or positive gradient series, with a

uniform distribution randomly determining which pattern

14

applied to each individual project, with 50 percent being

uniform and 50 percent being gradient (15:29). The

simulation calculated the following ranking criteria:

AEX = Annual equivalent excess of revenues over costsAEX/B, where B is the initial investment at time zeroPEX = Present equivalent excess of revenues over costsPEX/B, where B is the initial investment at time zeroPAYBACK = Time required to recover the initial investmentRANDOM = Randomly selecting projects for investmentIncr ROR = Rate of return on incremental investmentIncr AEX/B = AEX/B on incremental investmentIncr PEX/B = PEX/B on incremental investmentIncr PAYBACK = PAYBACK on incremental investment (15:16)

These criteria were applied to a set of ten independent

projects with four mutually exclusive alternatives for each

project. The measures of worth for the study were net

present value and rate of return. The results of the study

after five cycles of simulation are shown in Table 2. White

conQluded that:

1. The method employed to rank capital investmentalternatives does have an impact on the future netvalue of the firm.

2. The relationship between the cutoff rate ofreturn and the discount rate is important as itaffects the characteristics of the projects thatare selected by the discounted cash flow rankingmethods.

3. The data indicates that for the assumptions andparameters incorporated in this model, Incr ROR andIncr AEX/B provide a net value of the firm, and rateof return realized on initial funds supplied, thatis statistically significantly better than any ofthe other ranking criteria tested (Incr PEX/B, AEX,AEX/B, PEX/B, PEX, PAYBACK, Incr PAYBACK, and RANDOM).(15:77-78)

Whitaker developed a computer simulation to compare

payback period (PP) with the discounted cash flow criteria

of internal rate of return (IRR), profitability index (PI),

15

Table 2

Results Acheived through Five Cycles of Simulation

Net Value RORRank by in Millions Realized

AEX $10.31 25.14%AEX/B 10.53 25.52PEX 10.23 24.98PEX/B 10.52 25.34PAYBACK 7.81 22.48RANDOM 5.99 19.64Incr ROR 11.08 25.94Incr AEX/B 11.10 25.92Incr PEX/B 10.88 25.66Incr PAYBACK 6.46 20.48

(15:40)

16

and net present value (NPV) (14:1101-1111). The simulation

was performed for a 100 quarter (25 year) period, with

investment decisions being made quarterly. Cash flow

patterns for the projects were basically uniform with

adjustments made for varying levels of uncertainty. An

extensive discussion of the cash flow formulation can be

found in Whitaker (14:1102-1105). Whitaker investigated the

sensitivity of the different decision criteria to dependent

and increasingly variable cash flows. Cash flow dependence

is determined by:

the parameter a, the autocorrelation between cashflows. Variability is controlled by the parameter w,which is used to reflect the non-constant variance ofthe simulated cash flows (referred to as 'hetero-skedasticity'). (14:1107)

Project lives varied from four to 12 quarters with a maximum

of six projects available to choose each quarter (14:1107).

The results of the simulation are shown in Table 3. Whitaker

found that:

there were no significant differences between thealternative discounting methods of selection forthese simulated investments with any combinationof a and w (t - test). (14:1109)

However, the payback period method of selection resulted in

a significantly lower current value than all other methods

in all cases. Whitaker therefore concluded that payback

period is "an inferior method of selection" (14:1109).

4 aumnr

The literature has shown that although using ranking as

a method of selecting projects for capital investment may

17

Table 3

Results of Whitaker Study

Heteroskedasticity (w)

1.00 1.08 1.16

Crit x s x s x s

PP 128941 38367 126838 43076 123643 535740.0 NPV 186196 58441 187635 64500 188147 81239

PI 185279 54490 188207 62249 185826 78729IRR 190659 50548 190436 61500 189600 78099

A PP 127201 45375 127825 54188 123226 64184u 0.2 NPV 182987 60915 186813 71088 183486 88784t PI 182937 68615 185173 70658 184280 84072o IRR 191759 59331 193046 68687 186298 88493co PP 130230 56112 121074 63789 116756 74503r 0.4 NPV 181121 69509 183691 86138 176094 101874e PI 182937 68615 185173 83156 179698 1002821 IRR 185477 66542 188850 86053 192161 103667at PP 119567 66719 115849 79068 110812 82222i 0.6 NPV 182326 90652 183389 105244 170540 117627o PI 176650 84517 182084 102085 174303 115402n IRR 181688 88200 182296 103959 186967 124702

PP 109393 92119 109011 89001 117667 101321a 0.8 NPV 176130 109061 168816 122604 169085 154795

PI 175645 111121 174824 127079 168913 159337IRR 187220 111943 175052 129560 175662 162627

PP 110637 121389 110043 124560 98284 1179361.0 NPV 175002 163242 168248 167869 174470 215455

PI 172608 161686 172544 177979 182387 218485IRR 170172 161261 174110 185422 171069 211572

x - Average current value(s) after 100 iterations and $20,000outlay.s - Standard deviation of the 100 iterations.

(14:1108)

18

not result in the optimal economic mix for a firm, it is

still a popular and widely used method by a majority of

large or small businesses. Much interest and debate over

which economic criteria for a firm to use to maximize its

gain from capital investments continues in the literature.

Simulation provides a useful and cost efficient tool to

evaluate different decision rules and criteria over a period

of time that is sufficient to determine the long term

effects of capital investment decisions. It also provides

the only method to compare alternatives when actual imple-

mentation of a new alternative is not feasible without

knowing the actual results the new alternative would provide.

It is envisioned that the effects of a new ranking method

for the PIF program would be most apparent over a period of

years. The literature has shown that simulation is an

effective tool for the comparison of such decision rules and

will be used for the PIF program as described in the next

chapter.

19

The comparison of alternative methods of decision making

is particularly suited for simulation. Without simulation,

the only way to compare the effects of a new policy or

procedure would be to implement the change and observe the

results. It is obvious in the world of business, as well as

government, that such an action could be extremely costly.

In addition, methods of decision making, especially in

government, are frequently determined by regulations.

Without the ability to prove that a change in methodology would

result in substantial benefits, it is not likely that such

regulations would be changed. This is the case with the PIF

program, where the author wishes to compare an alternative

way of decision making without actually implementing it. If

substantial benefits could be realized, a change in the

current regulation may be merited. This is the reason

simulation is proposed for this study, "since the real

usefulness of the simulation technique is, by its very

nature, in studying such alternatives before their actual

implementation" (8:316).

Selection of the Model

In selecting an appropriate model to simulate the

generation of projects and the calculation of the economic

criteria used to rank and select projects for funding, three

alternatives were considered. They included a FORTRAN

20

computer program, a BASIC computer program, and a QUATTRO

spreadsheet simulation.

The author selected using a QUATTRO spreadsheet

simulation for the following reasons. First, the net

present value (NPV) and internal rate of return (IRR)

functions available with the QUATTRO professional

spreadsheet program is ideally suited for this study and

eliminates the need to write and debug complicated computer

subroutines. Second, the author determined that the

uniqueness of projects considered for funding in the PIF

program does not require the use of available probability

density functions of the BASIC or FORTRAN computer languages

for the generation of the project characteristics of cost,

savings, and life. These project characteristics are easily

generated using the QUATTRO random number generator based on

summary statistics of the FY85 PIF data. Third, the QUATTRO

spreadsheet program allows controlling of the random number

generator which enables the reproduction of the simulation.

Finally, the use of QUATTRO does not require extensive

knowledge in computer programming.

Research Design

The research design encompasses four phases as illus-

trated in Figure 1. Phase one consists of a review of the

FY85 PIF program database to determine the summary statis-

tics used to generate the simulated project characteristics

of cash flow pattern, cost, annual savings, life, and

manpower savings. Phase two entails generating the

21

Phase 1

Determine the FY85 PIF data summary statisticsfor project characteristics of project cashflow patterns, cost, annual savings, life, andmanpower savings.

Phase 2

Generate simulated database and perform rank-ing criteria calculations.

Phase 3

Rank and accept projects according to the DoDmethod and the Carry-over method.

Phase 4

Compare the net present values of the projectsselected by each method.

Figure 1. Simplified Research Design Flow Chart

22

simulation database which includes the number of projects to

generate, their cash flow patterns, costs, annual dollar

savings, and annual manpower savings. Phase two also

includes calculating the ranking criteria of return on

investment (ROI), internal rate of return (IRR), and cost

per manpower space saved (CPM) and also each project's net

present value (NPV). Phase three consists of ranking and

selecting the project mix for the DoD and the Carry-over

method. Phase four compares the mixes selected by the two

methods.

The review of the FY85 PIF program database centered on

gathering summary statistics in the areas of cash flow

pattern, project cost, annual savings, life, and manpower

positions saved. Summary statistics were deemed sufficient

based on the uniqueness of the projects. Table 4 contains a

summary of the statistics which comprised the basis for

generating the simulated project characteristics.

The FY85 PIF database consisted of 186 projects. In

reviewing these projects for cash flow patterns, the

following patterns were identified. First, 101 projects had

a constant annual savings. Second, 42 projects had constant

annual savings except for one year, which was either more or

less than the remaining annual savings and typically occurred

in either the first year or the last year of the projects'

operational lives. Third, 25 projects were found to have

increasing cash flow patterns and four projects had

decreasing cash flow patterns. Finally, 14 projects had

23

Table 4

FY85 PIF Program Summary Statistics

Percent ofProjects Generated Range

Annual Savings CashFlow Pattern

Constant 83.14Increasing 14.53Decreasing 2.33

Project Cost ($ Million) 0.104 - 15.53

Total Annual Savings($ Million) 0.300 - 537.30

Project Life (Years) 5 27

Manpower PositionsSaved 0 650

24

what the author considers erratic cash flow patterns which

did not follow any discernible pattern. For this study, the

author treated the cash flow patterns which were constant

except for one year as constant cash flow patterns and

discarded those which exhibited erratic cash flow patterns.

This resulted in three summary statistics to use in

generating simulated projects. Of the 172 projects

remaining after discarding the erratic cash flow patterns,

83.14 percent of the projects had constant cash flow

patterns, 14.53 percent had increasing cash flow patterns,

and 2.33 percent had decreasing cash flow patterns.

In reviewing the FY85 PIF database in terms of project

cost and annual savings, the costs ranged from

$.104 Million (M) to $15.53M and the total annual dollar

savings ranged from $0.3M to $537.3M (1:85). For this

study, the author elected to use the range of $.10M to $20M

as the summary statistic in determining the costs of the

simulated projects. In terms of annual savings, the author

selected the range of one-fourth (1/4) the cost of a project

plus an arbitrary amount ranging from $100,000 to $150,000.

This satisfies the payback period constraint of four years

necessary for a project to be considered for PIF funding.

The review of the FY85 PIF database in terms of project

life resulted in a minimum project life of five (5) years

and a maximum project life of twenty-seven (27) years. This

is the summary statistic used to determine the project lives

of the simulated projects.

25

In reviewing the database in terms of manpower positions

saved, it was found that fifty-one (51) (or 27.42 percent)

of the projects did not result in any manpower position

savings. The maximum manpower positions saved was 650.

Since manpower positions saved is a function of the annual

savings of a project, an ordinary least squares regression

analysis was performed, using QUATTRO, on the remaining 135

projects to determine a relationship for generating the

simulated data. The analysis resulted in the equation for

manpower savings of 8.4+.0133 (xi) where xi is the fourth

year annual savings for project i. The fourth year annual

savings was used to average the differences in annual

savings due to the type of cash flow pattern.

The anaJ-3-j resulted in a coefficient of determination

(R2 ) value jf 0.46. R-squared measures how well the

independent variable accounts for the variance in the actual

manpower savings data. Specifically, it denotes the ratio

of explained variance to total variance. The value of R2

ranges between zero and one with a value of one being

considered a perfect predictor. The relatively low value of

0.46 for R2 indicates that the annual savings is not a

significant predictor of manpower savings. However, it is

considered adequate for this study.

Two other major concerns in phase one consisted of

determining (1) the relative increase or decrease in annual

savings for the projects with increasing or decreasing cash

flow patterns, and (2) the length of time over the projects'

28

lives when the increasing/decreasing savings become

irrelevant. First, the author arbitrarily assumed that a

three (3) percent rate for increasing/decreasing cash flow

patterns is a reasonable rate. Secondly, the author

considered that after a period of time the estimate of

yearly savings becomes somewhat questionable due to the

uncertainty of future conditions. Also, continuing to

increase/decrease savings over the entire life of a long

life project can result in somewhat unrealistic values.

Therefore, the author opted for increasing/decreasing cash

flow pattern projects' annual savings at the three percent

rate for ten (10) years, after which the annual savings will

remain constant for the remainder of their lives. The ten

year point was chosen somewhat arbitrarily with the intent

of reaching a realistic annual savings profile for all

simulated projects. Table 5 summarizes the summary

statistics from the FY85 PIF data and those that will be

used to generate the project characteristics in phase two.

Overview of the QUATTRO Simulation Model

The simulation of the PIF project generation was accomp-

lished using the commercial software package QUATTRO: The

Professional Spreadsheet manufactured by Borland Inter-

national. The use of the spreadsheet greatly simplified the

need for knowledge in computer programming by the use of NPV

and IRR functions of the software. QUATTRO also has a

controllable random number generator which enables the

reproduction of the simulation and the setting of different

27

Table 5

Summary Statistic Comparison

FY85 PIF Data Simulation

Cost Range .104 - 15.53 .100 - 20($ Million)

Annual Savings .300 - 537.3[1 ] .125 - 5.15[2 ]

($ Million)

Project Life 5 - 27 5 - 27(Years)

Manpower Savings 0 - 650 8.4 + .0133 (xi)[ 3 ]

(Positions)[1] This is the range for total annual savings of a project.[2] This is the range for first year annual savings of a

simulated project.xi is the fourth year annual savings of a simulatedproject.

28

starting points in the random number sequence. This is

accomplished by the random number generator always starting

at the same position whenever QUATTRO is accessed on a

personal computer (PC) for the first time. To reset the

random number generator, the user simply exits QUATTRO and

then reloads it.

One of the disadvantages of using the spreadsheet is

that it required a large amount of user interface time to

complete the generation of the data. This was compounded by

the limited memory of the computer available to the author

which required the user to manually interface with the

spreadsheet when the availability of more memory would have

enabled a more complete automation of the PIF simulation and

greatly reduced the time required to generate the necessary

project charateristics. The average time required to

generate one run of data for the simulation was approximately

one hour and fifty minutes. One run consists of generating

five years of PIF projects. Each year consisted of anywhere

between one hundred (100) and two hundred (200) projects. A

detailed discussion of the model is presented next.

DeveloDment of the Simnlation Model

The overall logic and steps involved in performing the

simulation of the PIF program capital rationing problem is

illustrated in Figure 2.

The model begins with an initial budget ceiling of

$150M. It was assumed to be a realistic figure, based upon

29

---- Provide initial budget.

Generate projects with knowncost, life, annual savings

and cash flow pattern, andmanpower savings.

Perform calculations and rankprojects according to the DoDcriteria.

Select projects according tothe DoD method and theCarry-over method.

Calculate the net presentvalue of projects selectedby each method.

No Yes |Calculate net

Has ive earspresent valuebeenreacedof all pro-

jects selected

Sop

Figure 2. Simulation Logic Flow Chart

30

the apparent trend in annual funding profiles for the PIF

program as shown in Table 6.

The budget ceiling for each subsequent year remains

constant at $150M except for the funds remaining from the

previous year. Keeping the budget constant at $150M

eliminates one source of variability in determining the

significance of the difference between the two alternative

methods of project selection.

Given the initial budget ceiling, projects are then

generated and ranked in descending order of desirability

based upon the DoD criteria. Projects are then accepted

using the DoD method and the Carry-over method.

In the DoD method, projects are accepted until a project

is reached whose cost exceeds the budget remaining for that

year. That project is skipped and the next most desirable

project is funded, if possible. If it is not possible to

fund that project, the process is repeated until the funds

remaining are insufficient to accept any remaining projects.

The net present values of the projects selected are summed

and any budget remaining added to the next year's $150M

budget.

In the Carry-over method, the process is halted when the

first project whose cost exceeds the budget remaining is

reached. The net present values of these projects are

summed and the remaining funds are added to the next year's

$150M budget.

31

Table 6

Annual PIF Program Budget Ceilings

FY82 FY83 FY84 FY85 FY86

Budget Ceiling 90 121 129 136 139($ Million)

(1:15)

32

The next period begins with a new set of projects. The

process is repeated through five years. The sums of each of

the years' net present values are totalled. These sums are

used to evaluate the long term economic effectiveness of the

methods in achieving the objective of maximizing the net

present value of PIF projects.

This section has provided a basic understanding of the

PIF capital rationing process and the two alternative

methods to be compared through the use of a QUATTRO spread-

sheet simulation. The next section presents the detailed

procedures for using the spreadsheet to perform the simu-

lation. It is assumed that the reader is familiar with the

use of professional spreadsheet software in general.

The QUATTRO Simulation

Figure 3 illustrates a more detailed description of the

process described in the previous section as it applies to

using the QUATTRO software to perform the simulation.

The Random Number Generator

The simulation begins with initializing the random

number generator (RNG). For the first run, the RNG is set

by simply accessing QUATTRO. As mentioned previously, each

time QUATTRO is accessed the RNG begins at the same point.

Also, each run consists of generating five years of PIF

projects. It is desirable to set the RNG for two reasons.

First, to reproduce the simulation. Second, to minimize

possible duplication of projects with the same characteristics.

33

Initialize random number generator and year one budget ceiling.

Calculate x number of projects to generate and percentage of constant (C),

increasing (1, and decreasing D) cash flow patterns.

Generate x nuber of projects with calculated cost, life, first

year annual savings, manpower savings, and appropriate subsequent yearsavings according to C, 1, or D pattern.

Calculate DoD ranking criteria and net present value.

'IjRank projects in decreasing order of desirability according to DoD criteria.I

I IV

Accept projects until project is reached whose cost exceeds funds remaining.

Yes Using No

DODMethod >

Ne to next desirable project

Is cost No

less than fundsremaining?

No 3. all Yes Calculate annual netp- rojects

beenY

p

onsidered?J

~ ~ ~ ~ ~~lCalculate etpro' ugt ae toahe

presenttvalue.

Figure 3. Simulation Process Block iagram

34

The RNG is controlled by accessing QUATTRO and perform-

ing an @RAND function in cell Al. A Block Copy command is

then performed using cell Al as the source and designating a

destination block that exercises the RNG the desired number

of times. For example, if it is desired to start with the

eleventh random number, while in cell Al type @RAND, then do

a Block Copy with cell Al as the source and cells A2..AlO as

the destination blocks. Those cells could then be erased

then be erased or a desired file retrieved so that the next

time the @RAND function is exercised it will provide the

eleventh random number.

For this study, it was determined to begin each run by

starting the RNG 150 numbers further along the sequence than

the prior run. There were thirty runs done in this study

with the RNG set as shown in Table 7. This was performed on

a blank worksheet and then the template designed for this

study was retrieved and would access the RNG at the desired

starting point.

The QUATTRO template designed for this study contained

the following information used as a starting point for each

run:

1. Beginning budget2. Number of projects to simulate3. Number of projects with constant cash flows4. Number of projects with increasing cash flows5. Number of projects with decreasing cash flows6. Project number7. Project life8. Project cash flow pattern9. Project cost10. Project annual savings11. Manpower positions saved12. Sum of annual savings

35

Table 7

Random Number Generator Starting Points

SOURCE CELL DESTINATION STARTINGRUN *$ M@AND) BLOCK POINT

2 Al A2. .AlSO 1513 Al A2. .A300 3014 Al A2. .A450 4515 Al A2. .A600 6016 Al A2. .A750 7517 Al A2. .A900 9018 Al A2. .A1050 10519 Al A2. .A1200 1201

10 Al A2. .A1350 135111 Al A2. .A1500 150112 Al A2. .Al65O 165113 Al A2. .A1800 180114 Al A2. .A1950 195115 Al A2. .A2100 210116 Al A2. .A2250 225117 Al A2. .A2400 240116 Al A2. .A2550 255119 Al A2. .A2700 270120 Al A2. .A2850 285121 Al A2. .A3000 300122 Al A2. .A3150 315123 Al A2. .A3300 330124 Al A2. .A3450 345125 Al A2. .A3600 360126 Al A2. .A3750 375127 Al A2. .A3900 390128 Al A2. .A4050 405129 Al A2. .A4200 420130 Al A2. .A4350 4351

36

13. Net present value14. Internal rate of return15. Return on investment16. Cost per manpower space saved

The template contained equations for each of the project

characteristic items (7-12 above), DoD criteria (14-16 above)

and NPV (13 above) for one project only. Appendix A con-

tains a listing of the template entries by cell location.

Since the majority of the projects simulated have constant

cash flows, the annual savings equations in the actual

template were for constant cash flows. However, sample

entries for increasing and decreasing cash flow patterns are

included in Appendix A. Data generation for all subsequent

projects will be discussed shortly.

Data Generation

After setting the RNG and retrieving the template, the

first step in the process is to generate the number of

projects to simulate. The equation for the number of

projects to simulate is @INT(@RAND*101)+100 which yields a

random value between 100 and 200 projects to simulate and

resides in cell E3. This is accomplished by pressing the F2

function key on the PC keyboard. The F2 key performs an

edit function. Pressing F2 and then the Return key changes

the random number from what resides in current memory of the

template to the new starting point.

The next step in the process is to determine the number

of constant, increasing and decreasing cash flow patterns to

generate among the projects to simulate. The equation for

37

constant cash flow patterns is @ROUND(E3*0.8314,O) It

resides in cell H4. Cell E3 is the cell reference for the

total number of projects to simulate calculated above.

Similarly, the equation for increasing cash flow patterns is

@ROUND(E3*.1453,O) It resides in cell H5. Lastly, the

number of decreasing cash flow patterns is found by

subtracting the sum of the constant and increasing cash flow

patterns from the total number of projects to simulate, as

+E3-(H4+H5) It resides in cell H8. The use of the

@ROUND function above yields whole numbers of projects to

simulate. These values of numbers of cash flow patterns to

simulate are calculated automatically when the number of

projects to simulate is calculated.

The next step in the process involve the actual

generation of the simulated projects and their charac-

teristics. The first step is simply to number the projects.

This is performed in column A beginning in row 12. The

number 1 is entered in cell A12 and a Block Fill command is

used to increment the numbers by 1 up to the number of

projects to simulate.

Next, the project life is calculated in column B

starting in row 12. The equation is @INT(@RAND*23)+5

It gives a random project life between 5 and 27 years. This

equation is resident in the template. It is calculated for

the run by pressing the F2 and Return keys for project

number 1. A Block Copy command is used next to determine

the lives of the subsequent projects. Cell B12 is used as

38

the source cell, and the destination block is as appropriate

in column B beginning with cell B13 and ending in the

appropriate row to encompass the number of projects to

simulate.

The next step is to assign cash flow patterns to the

projects. A "C" resides in cell C12 of the template and

represents a constant cash flow pattern. Using the values

calculated above, a Block Copy command is used to assign the

cash flow pattern to the appropriate number of projects.

Then an "I" is inserted in the appropriate row in column C

to represent an increasing cash flow pattern. A Block Copy

command is used to assign the number of projects calculated

above an increasing cash flow pattern. Finally, the

remaining projects as calculated above are assigned a "D" to

represent a decreasing cash flow pattern.

The next step in the simulation is calculating the cost

of the projects. The equation resides in cell D12 for

project one and is entered as -@ROUND(@RAND*19901+100,1)

The values are in thousands and the equation will yield a

random cost between $100,000 and $20M rounded to the nearest

thousand dollars. Individual project costs are calculated

by pressing the F2 and Return keys for project one and

utilizing the Block Copy command for the subsequent

projects.

The next step is to calculate the first year annual

savings for each project. The equation for the first year

annual savings is *ROUND((-D12/4+(@RAND*50+100)),1) and

39

resides in cell E12. This results in a value of one-fourth

the cost of a project plus a random amount between $100,000

and $150,000. Again, it is calculated by pressing the F2

and Return keys and utilizing the Block Copy command for

subsequent projects.

The next step in the process is to calculate the

remaining annual savings for the life of each project. The

process varies according to the cash flow pattern of the

project and requires the majority of the user interfrce time

with the simulation. The savings for years two through

twenty-seven are included in columns F through AE.

For constant cash flow pattern projects, the equation is

simply the cell reference of the previous year. For

example, for project one, the savings for year one is in

cell E12. Then the equation for year two's annual savings

which resides in cell F12 is +E12. For year three, the

equation is +F12 and so on. The equation for year two

savings resides in cell F12 of the template for project one.

This is Block Copied down the column for the appropriate

number of projects identified in column C as constant cash

flow projects. Then for each individual project, the Block

Copy command is used with year two annual savings (cell F12

for project one) as the source cell and the destination,

block entered as appropriate across the row for the life of

that project. For example, project one has a life of 27

years. Then cell F12 would be the source cell and cells

G12..AE12 would be the destination block. This process is

40

continued for each project simulated with a constant cash

flow pattern.

The process is similar for projects with increasing and

decreasing cash flow patterns. The equation for year two

annual savings for an increasing cash flow project is three

percent more than the savings in year one. For example, the

equation for the year one savings for project 120 resides in

cell E131. Then year two's annual savings in cell F131 is

calculated by @ROUND(+El3l*1.03,1) The equation for

projects with decreasing cash flow patterns is similar with

a three percent decrease. For the example above, the year

two savings would be calculated by @ROUND(+E131*.97,1)

The process for the subsequent years differs somewhat

from that of the constant cash flow pattern projects. As

stated earlier in this chapter, after the tenth year the

projects change from increasing/decreasing patterns to

constant cash flow patterns. Therefore, the process differs

in how the subsequent years' savings are computed.

First, the equation for the second year annual savings

is entered for the first increasing cash flow project.

Then, a Block Copy command is used with that cell as the

source cell, and the destination block being the entire

block of cells for all increasing cash flow projects annual

savings through year ten. For example, projects 120 through

140 are increasing cash flow projects occupying rows 131

through 151. The equation for year two annual savings for

project 120 is entered in cell F131. Then a Block Copy

41

command is issued with cell F131 as the source cell and the

destination cells are F131 through N151. The same procedure

is used for decreasing cash flow projects. Following this

process, the next step is to return to the cell for year

eleven annual savings and enter the equation for a constant

cash flow pattern. For the above example, +N131 would be

entered in cell 0131. This copies the value from cell N131

to cell 0131. This is then Block Copied down the column for

all increasing/decreasing cash flow projects. The final

step for this phase of the process is to either use the

Block Copy command or the Block Erase command for each

individual project according to the life of that project.

The process just described is the preference of the

author only for calculating the annual savings for years

three through twenty-seven. There are many ways of

accomplishing the task and achieving the same results.

Also, it should be noted that with the use of nested IF

statements, the calculations of the annual savings for each

year could be made automatic. However, the random access

memory required for the use of such statements was more than

was available on the computer resources available to the

author.

The next step in the simulation is the calculation of

the manpower positions saved. The equation for the manpower

positions saved resides in cell AF12 of the template for

project one and is calculated as

*IF(@RAND<O.27,0,@INT(8.4+O.0133*Hl2) (1)

42

where H12 is the annual savings in year four. This ensures

that eighty-three percent of the projects simulated will

have some manpower savings and the remaining twenty-seven

percent will not. It is calculated again by pressing the F2

and Return keys for project one and using the Bluck Copy

command to calculate values for the rest of the projects

simulated. This concludes the discussion of cilculating

project characteristics for the simulation. The following

discussion is for the calculation of values of the DoD

ranking criteria.

Ranking Criteria and NPV Calculation

The next column in the template is AG and calculates the

sum of the annual savings for each project to facilitate the

calculation of the ranking criteria return on investment

(ROI) and cost per manpower space saved (CPM). It is

calculated with the @SUM function as @SUM(EI2..AE12) for

project one. The Block Copy command is then used to calcu-

late the sum for the subsequent projects.

The next column of the template is AH and cell AH12

contains the equation for calculating the NPV of project

one. The equation utilizes the *NPV function and is written

as @NPV(O.1,E12..AE12)+D12 where E12..AE12 is the block

containing the annual savings for project one and D12 is the

project cost (a negative amount). This calculates the NPV

at the discount rate of ten percent according to the DoD

requirements. The remaining projects' NPV's are calculated

with the Block Copy command.

43

The next criterion is the IRR for projects in column AI.

The syntax for the @IRR function is @IRR (guessrate,cashflowsjblock) where guess-rate is a value orreference to a value that gives the IRR function aplace to start, and the cash-flowsblock is the groupof cells holding the periodic cash flows estimatedfor the investment. (5:203)

For project one of the simulation the equation resides in

cell AI12 and is @IRR(.25,D12..AE12) . Values for

subsequent projects are calculated utilizing the Block Copy

command.

The next criterion is ROI and is the sum of the annual

savings divided by the sum of the costs. ROI is in column

AJ of the template and the equation for project one is in

cell AJl2. The equation is written as -AG12/D12 where

AG12 is the sum of the annual savings for project one and

D12 is the project cost. The negative sign is needed to

avoid getting a negative ROI caused by the project cost

being negative. ROI for the remaining projects are

calculated with the Block Copy command.

The final criterion is CPM and is calculated as the sum

of the project cost divided by the sum of the manpower

savings. CPM is calculated in column AK of the template.

The equation for the CPM of project one is in cell AK12 and

is written as @IF(AF12=O,1000000,-D12/AFl2) , where D12 is

the project cost and AF12 is the manpower positions saved.

For CPH, a lower value is more desirable than a higher value

as a ranking criterion. Therefore, those projects that have

zero manpower savings are set to an arbitrarily high value

of 100,000. The calculation of CPM for subsequent projects

44

is again accomplished using the Block Copy command.

Project Ranking

With the project characteristics and ranking criteria

calculated, the next step in the process is to rank the

projects in accordance with the DoD procedures. The

projects are ranked individually according to IRR, ROI, and

CPM. The ranks are then summed and the projects are ranked

according to the sum in ascending order of desirability.

In order to perform the ranking for the individual

criteria, a separate part of the spreadsheet is utilized.

Using a separate part of the spreadsheet is necessary to

avoid rearranging the projects prior to doing the final

ranking based on the sum of the individual rankings.

While in a column of the separate section of the

spreadsheet, the first step in the ranking process is to

perform a Block Fill command corresponding to the number of

projects for the particular simulation run. An alternative

method is to use the Block Copy command to copy the project

numbers from column A of the spreadsheet to the current

column. Next, the values of an individual ranking criterion

are copied from the worksheet to a column to the right of

the current column. The projects are then ranked using the

Advanced Database Sort command.

The block of data to be sorted contains the columns with

the project numbers and their ranking criteria plus an

additional column to the right of these two columns. The

purpose of the additional column will be discussed shortly.

45

The sort key is the column containing a particular ranking

criterion. The sort order is determined by the particular

criterion being ranked. The IRR and ROI criteria are ranked

in descending order based on a higher value of IRR or ROI

having a higher level of desirability. The CPM criterion is

ranked in ascending order based on a lower value of CPM

having a higher level of desirability.

With the project numbers now sorted according to a

particular criterion, they are assigned their rank utilizing

the Block Fill command in the third column mentioned

previously. The projects are then resorted with the sort

key being the column containing the project numbers in

ascending order. This results in the projects being

arranged in their original order.

The final step in the individual ranking procedure is to

copy the values from the ranking column to a column in the

spreadsheet. Four columns were added to the original

template to accomodate the rankings. Columns AL, AM, and AN

contain the rankings for IRR, ROI and CPM respectively.

Column AO of the template contains the sum of the

individual rankings. The final step in the ranking pro-

cedure is now performed. The entire spreadsheet is sorted

with the sort block being columns A through AO. The

projects are sorted with column AO being the sort key in

ascending order. The projects are now ranked according to

46

the DoD procedures and the final step of the simulation is

performed. The final step of the simulation is project

selection.

Project Selection (The DoD Method)

The first step in the project selection procedure is to

enter the beginning budget. The beginning budget is a

constant $150M in year one for each run. This value is

entered in cell AP10 of the template for selecting projects

according to the DoD method. Column AP is used to calculate

the budget remaining after each project is selected. The

first project is selected by subtracting the cost from the

beginning budget. The equation is entered in cell AP12 as

+AP10+D12 where AP10 is the beginning budget and D12 is

the project cost. The result of the equation is the budget

remaining. Note that row eleven is used for separating the

data from the column headings. Therefore project two is

selected by subtracting the cost from the budget remaining

with the equation in cell API3 being +AP12+D13 where AP12

is the budget remaining after selecting project one and D13

is the project two cost. This equation is then copied down

column AP using the Block Copy command.

After performing the Block Copy command the values in

column AP are examined to find the first negative result.

This is the point at which the project cost exceeded the

budget remaining. The negative values are then erased from

the spreadsheet with the Block Erase command.

The next step in project selection is to examine the

47

project data near the point where the budget remaining

charged from positive to negative (the transition point).

The data are examined to determine if there are ties in the

project rankings which could impact the project selection

order. According to the DoD procedures, in the case of a

tid in project ranking the project with the highest IRR is

selected first.

The reason for examining the data near the positive to

negative transition point is clear. Ties do not pose a

problem if all projects that are tied can be funded because

the net budget remaining would be the same regardless of

which projects are selected first. However, near the

transition point, a tie can result in the funding of one

project precluding the funding of subsequent projects.

Therefore, it is near the transition point where the data

must be examined. If the examination shows a tie exists and

a project with a lower IRR was selected first, the equations

were changed manually to comply with the DoD procedures.

With the negative values of the budget remaining erased,

the data are now manually searched to simulate the DoD

selection method of skipping. Utilizing the spreadsheet

window function, the project costs are displayed simul-

taneously with the budget remaining and project rankings.

The remaining project costs are searched to find the first

project whose cost is less then the budget remaining. This

project cost is subtracted from the budget remaining and the

process is repeated until all projects for that year have

48

been searched and funded if possible. The budget remaining

is then carried over to the next year budget of $150M.

Project Selection (The Carry-Over Method)

The project selection procedure for the Carry-over

method is identical to the process described above except

no projects are skipped. The beginning budget is entered in

cell AR1O of the template. Project costs are then

subtracted from the budget until the budget remaining in

column AR transitions from positive to negative. The

negative budget remaining is erased and the remaining budget

is carried over to the next years budget of $150M.

Net Present Value Calculations

The final step in the simulation is to calculate the NPV

of the projects selected. This is accomplished in columns

AQ and AT of the spreadsheet for the DoD method and the

Carry-over method respectively. The NPV of the projects was

calculated previously in column AH of the spreadhseet. The

NPV of the projects that were selected is copied into

column AQ or AT as appropriate using the Block Copy command.

The total NPV of all projects selected for that year is then

calculated using the * SUM function.

The project selection and NPV calculation process is

repeated through five years for each of the thirty runs of

the simulation. The five year total of the NPV for each

year is calculated. This five year NPV total is used to

test the research hypothesis.

49

A sample of an annual spreadsheet for the entire process

is presented in Appendix B.

Hvothesis Testing

The two different methods of project selection are

performed on identical sets of available projects. By

repeating the selection process of a five year period for

thirty cycles, a paired sample t test can be used to test

the statistical significance of the difference between the

two alternative methods.

In order to perform the paired sample t test, the

differences (d) between the five year NPV totals of the

Carry-over method and the DoD method must be calculated. A

basic assumption of the paired sample t test is that the

differences are normally distributed (3:344). The normality

assumption will be tested visually with a normality plot.

Assuming that the differences are normally distributed,

the paired sample t test will be used to test the

hypothesis:

Ho: the mean of the differences (d), NPV(Carry-Over) -NPV (DoD), 0.

HA: the mean of the differences (j), NPV(Carry-Over) -NPV (DoD), > 0.

HA: the mean of the differences (d), ofNPV (Carry-Over) -NPV (DoD) < 0.

The test statistic is computed as:

d

t paired - (2)SD/ n

where d and SD are the sample mean and standard deviation,

50

respectively, of the d's and n is the sample size. For a

one-tailed t test, the null hypothesis will be rejected in

favor of the appropriate alternative hypothesis if the

observed value of t is greater/less than or equal to the

critical value of t. The paired t test will be tested at

significance levels of 0.10, 0.05, 0.025, and 0.01. An

extensive discusion of the paired sample t-test can be found

in Devore (3:343-350).

Sensitivity Analysis

An extensive sensitivity analysis could not be

accomplished for this study based upon the time limitations

imposed by the nature of the simulation. The sensitivity

analysis is limited to the use of one economic criterion as

the-sole ranking criterion used to select PIF projects. The

economic criterion selected is the excess profitability

index (EPI). The EPI for a project is defined as it's NPV

divided by it's cost. The EPI is used to compare the use of

an economic criterion with the use of the DoD non-economic

criteria. EPI was chosen based upon the results of the study

performed by Christensen (1). Christensen showed that

EPI resulted in "the mix with the largest NPV of the ranking

methods compared" (1:109).

The data pertinent to ranking the projects based solely

on EPI were extracted from the spreadsheets and a separate

selection process was performed. The pertinent data

included the project numbers, costs, and NPV's. The EPI was

calculated and the projects were ranked according to EPI in

51

descending order. The selection of projects was performed

using the same processes described originally. Ties in EPI

were broken by the project with the highest IRR taking

precedence.

The difference between the total NPV of projects

selected using EPI as the ranking criterion and the total

NPV of projects selected using the DoD criteria is compared.

The NPV's are compared the comparison is purely descriptive

in nature for both the DoD and Carry-over methods of

selection.

Sumary

This chapter describes the procedures used to generate a

spreadsheet simulation of the PIF program. The simulation

consists of three phases 1) project generation, 2) project

ranking and 3) project selection. Projects are selected

according to two alternative methods. The DoD method

simulates the DoD method of skipping projects until the

available budget is exhausted. The Carry-over method

simulates an alternative method of project selection which

does not allow skipping. The process is simulated for a

five year period of project selection. The five year totals

of the NPV of the projects selected by each method are

compared. Finally, a third method is used to oompare the

sensitivity of the goal of maximizing NPV to the use of

economic and non-economic criteria for ranking projects.

The results of the simulation are described in Chapter IV.

52

IV. Findings and Discussion

The five year NPV totals for each selection method, and

their differences, are given in Table 8 for each of the

thirty runs of the simulation. Appendix C contains a com-

plete listing of the annual NPV's for the projects selected

for each of the thirty runs.

The objective of this study is to test the hypothesis

that the total NPV of projects selected by the Carry-over

method is greater than the total NPV of the projects

selected by the current DoD method. Table 8 illustrates

that the total NPV of the projects selected by the Carry-

over method is greater than the total NPV of the projects

selected by the DoD method in only five of the thirty runs.

A summary of the descriptive statistics for each of the

methods is given in Table 9. These values were calculated

using STATISTIX. STATISTIX is an interactive statistical

analysis program for microcomputers manufactured by NH

Analytical Software. The average NPV of the projects

selected by the Carry-over method is $1.179 billion (B).

The average NPV of the projects selected by the DoD method

is $1.184B. The NPV of the Carry-over method is less than

the NPV of the DoD method by an average of $5.135M. The

next section describes the results of the statistical

analysis of the difference between the two methods.

53

Table 8

Five Year NPV Total Results of the Simulation

Run NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

-1 1,188,954.2 1,203,842.2 -14,880.02 1,211,444.2 1,228,397.6 -16,953.43 1,184,029.8 1,189,538.5 - 5,508.74 1,155,879.9 1,158,945.5 - 3,065.65 1,211,671.7 1,213,868.3 - 2,196.66 1,185,669.9 1,191,708.8 - 6,038.97 1,154,186.2 1,158,487.3 - 4,301.18 1,218,478.3 1,223,654.7 - 5,176.49 1,182,833.2 1,198,986.9 -16,153.7

10 1,188,526.1 1,186,925.9 1,600.211 1,146,679.4 1,157,455.4 -10,776.012 1,161,915.7 1,189,371.0 - 7,455.313 1,131,968.0 1,138,540.3 - 6,572.314 1,173,888.7 1,168,121.9 5,766.815 1,141,589.7 1,144,060.7 - 2,471.016 1,193,535.9 1,192,981.5 554.417 1,147,438.9 1,147,006.4 432.518 1,153,879.9 1,160,381.1 - 6,501.219 1,202,328.9 1,207,225.8 - 4,896.920 1,207,472.3 1,209,567.6 - 2,095.321 1,186,253.1 1,191,536.7 - 5,283.622 1,205,006.2 1,205,429.6 - 423.423 1,191,794.5 1,195,351.4 - 3,556.924 1,186,637.8 1,186,559.3 78.525 1,169,045.6 1,179,890.3 -10,844.726 1,189,247.2 1,198,909.1 - 9,661.927 1,160,464.3 1,165,708.0 - 5,243.728 1,159,053.6 1,160,865.0 - 1,811.429 1,169,145.6 1,174,524.6 - 5,379.030 1,184,965.8 1,190,187.3 - 5,221.5

54

Table 9

Descriptive Statistics of Simulation Results

(Five Year NPV Totals)

NPV NPV Difference(Carry-Over) (DoD) (Carry-over - DoD)($ Thousand) ($Thousand) ($ Thousand)

Mean 1.179E+06 1.184E+06 - 5.135E+03

StandardDeviation 2.275E+04 2.361E+04 5.160E+03

Median 1.184E+06 1.189E+06 - 5.199E+03

Minimum 1.132E+06 1.139E+06 - 1.695E+04

Maximum 1.218E+06 1.228E+06 5.767E+03

55

Normality Testinf

In order to conduct a paired sample t test on the

simulation data, the assumption of normality must be proven.

STATISTIX tests for normality using WILK-SHAPIRO/RANKIT

PLOTS.

WILK-SHAPIRO/RANKIT PLOTS examines whether a vari-able conforms to a normal distribution. A rankitplot of the variable is produced, and an approxi-mate Wilk-Shapiro normality statistic, the Shapiro-Francia statistic, is calculated. (12:84)

In simple terms, in examining the output of a WILK-

SHAPIRO/RANKIT PLOT, the plot of the variable "Rankits"

versus the variable of interest should appear to be linear

if the sample data are from a normal distribution. For the

variable "Rankits", "the i-th rankit is defined as the

expected value of the i-th order statistic for the sample,

assuming the sample was from a normal distribution" (12:85).

In this case, the variable of interest is d, the difference

between the total NPV of the Carry-over method and the total

NPV of the DoD method for each run.

Also, in examining the output of the WILK-SHAPIRO/

RANKITS PLOT, the approximate Wilk-Shapiro statistic pro-

vides a measure of the strength of the normality assumption.

In simple terms, a small value of the Wilk-Shapiro statistic

is an indication of non-normality (12:8.5). Although a

small value is not defined, a value of 1 could be viewed as

the sample coming from an exactly normal distribution.

Therefore, a value close to one is desired. For this stuy,

close is defined as greater than 0.9.

56

Figure 4 shows the output of the WILK-SHAPIRO/RANKITS

PLOT for the differences between the total NPV of each run.

Examination of the figure shows no evidence of non-

normality. The approximate Wilk-Shapiro statistic value of

0.9491 and the approximate linear trend support the con-

clusion that the sample data validates the assumption of

normality and a paired sample t test can be performed.

Paired Rample T Test

The paired sample t test was used to determine the

statistical significance of the difference between the two

alternative methods of project selection. A one tailed t

test was used for this study to form the rejection region

for the null hypothesis HO: NPV (Carry-Over) -NPV (DoD)

0. -The test was conducted for levels of significance of

0.10, 0.05, 0.025, and 0.01. Table 10 contains the critical

t values for a one tailed t test with HA > 0 and HA < 0 at

the various levels of significance. These values were

obtained from table A.5 of Devore (3:635) with = 29, or

one less than the sample size of 30 for this study.

If the computed value of t is greater than the critical

t values for HA > 0, the null hypothesis is rejected in

favor of the alternative hypothesis that the total NPV

(Carry-over) minus the total NPV (DoD) is greater than 0.

If the computed value of t is less than the critical t

values for HA < 0, the null hypothesis is rejected in favor

of the alternative hypothesis '-at the total NPV (Carry-

over) minus the total NPV (DoD, is less than 0.

57

Rankits vs Difference

RANKITS3.0 +

++

+

1.0 +..22

+2+-1.0 + 2 +

+

-3.0 +-+--------------+--------------------------

-1.8 -1.2 -0.6 0.0 0.6Difference X 10E4

APPROX. W'ILK-SHAPIRO 0.9491 30 CASES PLOTTED

Figure 4. Normality Plot of the Results

58

Table 10

Critical t Values for the t Distribution

Level of Significance 0.10 0.05 0.025 0.01

Critical t Value

HA > 0 1.311 1.699 2.042 2.457HA < 0 -1.311 -1.699 -2.042 -2.457

(3:635)

59

Hypothesis Rejected

The paired sample t test was computed with STATISTIX.

The computed t value was -5.45. From the values given in

Table 10, this results in the null hypothesis being rejected

in favor of the alternative hypothesis HA: NPV (Carry-

Over) -NPV (DoD) < 0 at all levels of significance.

Therefore, it can be concluded that the Carry-over method of

project selection does not result in greater savings to the

government than the current DoD method.

Sensitivity Analysis

A summary of the five year NPV totals for the projects

selected using EPI as the only ranking criterion are given

in Table 11 for each of the selection methods. Also,

included in Table 11 is the difference between the total NPV

(Carry-over) and total NPV (DoD). Table 12 provides the

summary statistics obtained using EPI as the only ranking

criterion. Table 13 includes the summary statistics for

both types of ranking criteria.

Using EPI as the only ranking criterion did not signifi-

cantly affect the results of the simulation. The total NPV

using the DoD method was less than the total NPV using the

Carry-over method in only 9 of the 30 runs. The nine runs

is an increase from the five using the DoD ranking criteria,

but still a minority of the cases.

However, using EPI as the only ranking criterion did

increase the total NPV for both methods of project selection

compared to the DoD ranking criteria. This result is

6o

Table 11

Five Year NPV Totals Using EPI as the Sole Ranking Criterion

Run NPV NPV Difference(Carry-over) (DoD) (Carry-over - DoD)($ Thousand) ($ Thousand) ($ Thousand)

1 1,269,520.7 1,273,044.2 - 3,523.52 1,276,560.4 1,285,609.1 - 9,048.73 1,221,330.3 1,235,285.7 -13,955.44 1,231,567.6 1,232,740.3 - 1,172.75 1,289,347.4 1,288,397.3 950.16 1,252,136.5 1,257,501.0 - 5,364.57 1,230,380.3 1,228,686.8 1,693.58 1,291,073.8 1,290,307.4 766.49 1,240,934.4 1,243,990.1 - 3,055.7

10 1,242,537.3 1,246,142.4 - 3,605.111 1,218,656.5 1,230,725.8 - 12,069.312 1,260,558.6 1,264,654.0 - 4,095.413 1,193,096.0 1,193,689.7 - 593.714 1,240,899.8 1,244,066.1 - 3,166.315 1,215,435.4 1,213,126.8 2,308.616 1,233,289.1 1,241,117.1 - 7,828.017 1,204,896.6 1,212,421.6 - 7,525.018 1,222,336.7 1,224,117.0 - 1,780.319 1,248,980.7 1,268,599.1 - 19,618.420 1,276,935.1 1,282,134.6 - 5,199.521 1,232,389.1 1,232,133.5 255.622 1,255,068.8 1,251,486.9 3,581.923 1,256,223.5 1,255,958.9 264.624 1,259,161.8 1,266,136.0 - 6,974.225 1,245,425.2 1,248,453.6 - 3,028.426 1,255,195.9 1,263,772.8 - 8,576.927 1,220,475.3 1,235,482.4 - 15,007.128 1,222,452.3 1,221,680.5 771.829 1,228,658.6 1,235,961.2 - 7,302.630 1,258,084.3 1,253,208.1 - 4,876.2

61

Table 12

Descriptive Statistics of Simulation ResultsUsing EPI as the Ranking Criterion

NPV kNPV Difference(Carry-Over) (DoD) (Carry-over - DoD)(Thousand) ($Thousand) ($ Thousand)

Mean 1.243E+06 1.247E+06 - 4.234E+03

StandardDeviation 2.397E+04 2.384E+04 5.773E+03

Median 1.242E+06 1.245E+06 - 3.345E+03

Minimum 1.193E+06 1.194E+06 - 1.962E+04

Maximum 1.291E+06 1.290E+06 4.876E+03

Table 13

Descriptive Statistics of Simulation Results(Comparison of DoD and EPI Ranking Criteria)

NPV NPV Difference(Carry-over) (DoD) (Carry-over-DoD)($ Thousand) ($housand) ($ Thousand)

Criteria

Mean DoD 1.179E+06 1.184E+06 - 5.135E+03EPI 1.243E+06 1.247E+06 - 4.234E+03

StandardDeviation DoD 2.275E+04 2.361E+04 5.160E+03

EPI 2.397E+04 2.384E+04 5.773E+03

Median DoD 1.184E+06 1.189E+06 - 5.199E+03EPI 1.242E+08 1.245E+06 - 3.345E+03

Minimum DoD 1.132E+06 1.139E+06 - 1.695E+04EPI 1.193E+06 1.194E+06 - 1.962E+04

Maximum DoD 1.218E+06 1.228E+06 5.767E+03EPI 1.291E+06 1.290E+06 4.876E+03

62

consistent with Christensen. The average total NPV using

the DoD method of project selection increased from $1.184B

to $1.247B or a difference of $63M. The average total NPV

using the Carry-over method of selection increased from

$1.179B to $1.243B or a difference of $64M. However, the

difference between the two methods of project selection

still showed that the total NPV of the Carry-over method was

less than the total NPV of the DoD method by an average of

$4.234M.

Discussion

This chapter has presented the results of a simulation

comparing two alternative methods of project selection for

the PIF program. The results were statistically significant

in rejecting the research hypothesis that the use of the

Carry-over method would result in a greater total NPV than

the current DoD method of project selection. In contrast,

the results determined significantly that the DoD method

results in a greater total NPV than the proposed Carry-over

method.

The results also show that the use of an economic

criterion as the only basis for ranking does not affect the

research hypothesis. However, the sensitivity analysis did

show that the use of an economic criterion results in a

greater total NPV than the use of non-economic criteria.

Based on a review of the data, the reasons that the

Carry-over method did not result in a greater total NPV than

the DoD method seem to be based upon the project

63

characteristics. Typically, the budget remaining after

selecting projects using the Carry-over method was not large

enough to enable the funding of the project that halts the

Carry-over method of project selection and begins the DoD

method of skipping. For example, if $10M was carried over

from the first year's budget to the second year's budget,

the cost of the first project which could not be funded by

either method in the second year would exceed $10M.

Therefore, the additional funds that were not used in a

given year for the Carry-over method would not necessarily

provide a benefit in the subsequent year and would be

carried over yet another year before a benefit could be

realized. Meanwhile, the DoD method is continuing to

maximize the use of the annual budget for each year. When

the funds that were carried over using the Carry-over method

did provide a benefit, the NPV of the project(s) selected

was not large enough to make up the difference of the NPV of

the projects that were selected in the current and previous

years using the DoD method.

Summary

This chapter has described the results of the simulation

of the PIF program capital rationing problem. Two alterna-

tive methods of selecting projects were compared to

determine if the present method of skipping economically

attractive projects to maximize the use of an annual budget

results in a lower long term NPV than could be realized if

skipping was not allowed and unused funds could be carried

64

over wtihout penalty.

The results show that the current method of project

selection does not result in a lower long term NPV than a

Carry-over method. However, the results do show that the

current method of using non-economic ranking criteria does

not provide a greater long term NPV than using an economic

criteria as a basis for project selection. Chapter V

presents a summary of this study and some suggestions for

further research.

65

V. Conclusions and Recommendations

This study compared two capital rationing heuristics as

they apply to the PIF program. The comparison was accomp-

lighed using a QUATTRO spreadsheet simulation. The specific

research question addressed is as follows: The NPV of

projects selected for the PIF program by the Carry-over

method (no skipping) is greater than the NPV of projects

selected by the current DoD method (which allows the

skipping of projects until budgeted funds are exhausted).

Conclusions drawn from the results of the simulation

will first be presented followed by recommendations for

further research suggested as a result of this study.

Conclus ions

The results of the simulation indicate that the NPV of

projects selected by the Carry-over method is not greater

than the NPV of projects selected by the current DoD method.

In fact, the paired sample t test showed that the NPV of

projects selected by the DoD method is statistically signif-

icantly greater than the NPV of projects selected by the

Carry-over method. The NPV of projects selected refers to

the total NPV of projects selected through a five year time

period.

The sensitivity analysis showed that, regardless of the

method of project selection, the process of ranking

66

projects based on the DoD non-economic criteria yields a

suboptimal economic mix of projects. The NPV of projects

selected by using an economic criterion alone results in a

more economically attractive mix of projects. This shows

that more savings can be realized by the PIF program through

either changing the criteria used to rank projects, or as

shown by Christensen, through the use of integer

programming.

Recommendations for Further Research

This study suggests several areas for further research.

One possibility is to perform the comparison of the two

methods using five consecutive years of actual PIF data.

This would eliminate the inaccuracies of using summary

statistics to generate project charateristics.

In the absence of actual PIF data, another possibility

is to replicate the simulation with varying budget ceilings

to determine the sensitivity of the methods to the funds

available.

Another possibility for replication is to perform the

simulation for a longer time period. Although five years

was used for this study and was considered to be long term

in an economic sense, it may not have been long enough to

determine conclusively that the Carry-over method results in

less economic savings than the DoD method. From a practical

viewpoint, using five years as the time period simulated may

introduce a measure of bias to the results in favor of the

DoD method. The DoD method maximizes the use of the budget

67

and NPV of projects selected each year. The Carry-over

method begins at a disadvantage since the beginning budgets

are equal and skipping is not allowed. The disadvantage is

measured in terms of NPV of projects selected. The funds

remaining using the Carry-over method may not be sufficient

to utilize in the second year and are carried over to the

third year. The beginning budgets are then relatively equal

for the fourth year simulated, again putting the Carry-over

method at a disadvantage. The disadvantage, again, may or may

not be made up by the funds carried over to the fifth year

budget. A simulation of perhaps twenty or thirty years

could determine an actual pattern or dampen out the effects

of the disadvantage over the longer time period.

68

Appendix A: Sample Template Entries by Cell Location

This appendix contains a listing of the cell contentsas they are entered into the spreadsheet in order to performthe simulation. The entry locations are identified by theircolumn letters and row numbers along the top and left handsides respectively. The entries shown are intended toallow the reader the ability to recreate the simulation byshowing the equations as they are actually entered into thespreadsheet and noticing the differences in equationsaccording to the type of cash flow pattern a projectexhibits. Appendix B contains sample output of a typicalspreadsheet.

A BC D

1 YEAR i RUN 3 DoD2 ENTER BEGINNING BUDBET > CARRY-OVER3 THE NUMBER OF PROJECTS TO SIMULATE4 CALCULATE THE NUMBER OF PROJECTS WITH CONSTANT CASH FLOWS =5 CALCULATE THE NUMBER OF PROJECTS WITH INCREASING CASH FLOWS =6 CALCULATE THE NUMBER OF PROJECTS WITH DECREASING CASH FLOWS =B

9 PROJECT CASH FLOW PROJECT10 NUMBER LIFE PATTERN COST11

12 1 @INT(@RANDt23)+5 C -@ROUND(RANDt199OI+ O0,1)13 121 #INT(@RAND823)+5 I -@ROUND(@RAND$I?01+100,1)14 141 @INT(@RAND123)+5 D -@ROUND(@RANDt19901+100,1)15

69

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

E F 800

2 150000L 150000

3 @INT(RAND101)+1004 ROUND(+E3t143/172,0)

5 @ROUND(4E3125/172, 0)6 +E3-@SUM(H4+HS)78

9 SAVINGS SAVINGS SAVINGS SAVINGS10 YEAR #1 YEAR #2 YEAR #3 YEAR #4

12 @RDUND((-D12/4+(@RAND50+100)),I) +E12 +F12 +61213 @ROUND((-D13/4+(IRANDt5O+0)),I) @ROUND(+E13t1.03,1) @RDUND(+F13tI.03,1) @ROUND(+613$1.03,!)14 @ROUND((-D14/4+(@RAND50+I00)),) @RGUND(+E1410.97,1) @ROUND( F1410.97,1) @ROUND( 61410.9?,I)15161

70

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

K L

2

4

6

89 SAYINGS SAVINGS SAVINGS SAVINGS

10 YEAR #5 YEAR 16 YEAR #7 YEAR H8

12 +H12 +112 +J12 +K12POeRUND (+HI 3$1.03, 1) @R0UND(+II31!.03,I) POaUND (+JI11.03, 1) MOQUND (+KI70tI.03, 1)

14 @ROuND(+H140.97,I) @ROUND(+I14tO.97,1) @ROUND(+Jl4t0.97,i) @R0UND(+K14t0.97,I)

7 1

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

1

3456

89 ....... SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS

10 YEAR #9 YEAR 110 YEAR Ii1 YEAR 112 YEAR 113 YEAR 114 YEAR 1151 1 ------------------ -------------------------------------------------------------------------12 4112 M12 +N12 +012 +P12 +012 +R1213 @ROUND(+LI31.03,i1 @R0UND(+13i.03,1) +N13 +013 +P13 +913 +1314 @RGUND(+L1410.97,1) @RDUND(+11410.97,i) +N14 +014 +P14 +014 +R141516

72

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

T U v w x Y Z AA AB

456

9 SAVINGS SAVINGS SAVINGS SAY!NBS SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS10 YEAR #16 YEAR 117 YEAR 41R YEAR 819 YEAR #20 YEAR #21 YEAR 122 YEAR #270 YEAR 124

I2 + S12 +T11 + U12 + v IIL + W12 +X12 +Y 121 + Z12 + A A1213 +313 1TI1 + U13 +1 +1 +X13 +YI3 +IL3 4AA13

14 +514 +T14 +U14 +V14 41j4 +114 +Y14 +Z14 +Aj4

16

7 3

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

AC AD AE AF AG TI

234567 ---------------8 MANPOWER SUM OF9 SAVINGS SAVINGS SAVINGS POSITIONS ANNUAL

10 YEAR 125 YEAR 126 YEAR #27 SAVED SAVIN6SIi

12 +ABi2 +ACI2 +AD12 @IF( RAND(=0.27,0,9INT(B.4+0.0133IHl2)) @SUM(EI2..AEl2)

13 +ABI3 AC13 +ADI3 @IF(@RAND(=0.27,0,@INT(B.4+0.0133?H13)) @SUM(E13..AE13)

14 +AB14 +AC14 +AD14 @IF(@RAND<=0.27,0,@INT(B.4+O.O332H14)) @SUM(El4..AE14)

1516

74

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

AH Al AJ

4

6

7B

9I0 NPV IRR RO

12 @ROUND(@NPV(O.I,EI2..AE121+D12,1) @ROUND( IRR(O,3,D12..AE12),3) @ROUND(-ASl2/D12,3)13 @ROUND(@NPY(O. IEI3.AE13)+D13,I) ROUND( IRR(O.3,D13..AE13),3) @ROUND(-AB13/D13,3)

14 @ROUND(RNPV(O.1 E14..AEi4)+D14,1) ROUND(@IRR(O.3,D14..AE14),3) iROUHD'-AG14/Di4.3)

1516

75

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

AK AL AM~ AN AD AP

4c

RANK RANK RANK TOTAL BEGINNINGBY BY BY DoD BUDBET(DoD)

c0 IRR ROI CPM RANKING +El1 1 . . . . . .. . .. . .. .. . .. . . . . . . . . . . . .. . . .. . . .. . .- - . . . .. . . . .. . . .. . . . .. . . . .. . . . .. . . .. . . . . . . . . .

12 @ROUND(@IF(AF12=O,IOOOOO,-DI2/AF12),3) 2 2 2 6 +APIO+D1213 *RaUND(@IF(AFI3=O,1OOOOO,-DI3/AF13),3) 3 1 5 9 +AP12+D1314 @ROUND(@IFCAF14=O,1OOOOO,-DI4/AF14),3) 1 3 6 10 +AP13+D1415167

76

SAMPLE TEMPLATE ENTRIES BY CELL LOCATION

4567B TOTAL BEGINNING TOTAL9 NPV BUDGET (CARRY-OVER) NPV

10 DoD +E2 CARRY-OVER1 1 - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

12 10598,3 +ARIO+D12 10598.313 22454.5 +ARI2+D13 22454.514 4103.6 +ARI3+D14 4103.615

16 @SUM(AO2 .A014) @SUM(AH2 ..AT14)

77

Appendix B: Sample Simulation Out

This appendix contains sample output from thesimulation. The sample is the output from Year 5 of Run 3.Although 102 projects were simulated for this year, onlyare shown for the ease of printing. Enough output isincluded to illustrate the entire process.

78

SAMPLE SIMULATION OUTPUT

YEAR 5 RUN 3 DoD $150,461.6

ENTER BEGINNING BUDGET > CARRY-OYER $154,102.7THE NUMBER OF PROJECTS TO SIMULATE 102

CALCULATE THE NUMBER OF PROJECTS WITH CONSTANT CASH FLOWSCALCULATE THE NUMBER OF PROJECTS WITH INCREASING CASH FLOWS =15CALCULATE THE NUMBER OF PROJECTS WITH DECREASING CASH FLOWS =

PROJECT CASH FLOW PROJECT SAVINGS SAVINGS SAYINGS SAYINGS SAYINGSNUMBER LIFE PATTERN COST YEAR 11 YEAR 12 YEAR 13 YEAR 14 YEAR #5

81 9 C (103.0) 152.2 15.2 152.2 152.2 152.218 26 C (212.8) 189.7 189.7 189.7 189.7 189.794 13 1 (226.1) 158.9 163.7 168.6 173.7 178.992 19 I (444.0) 233.2 240.2 247.4 254-. S 2 6.461 27 C (1,909.6) 624.5 624.5 624.5 624.5 624.5

38 26 C (2,294.0) 688.1 688.1 688.1 62.1 688.190 13 I (1,265.0) 456.4 470.1 484.2 513.757 c C98 09r i ......- l .8cC 1099.8109953 .5 (3,877,7) 1099.8 1099.8 1099.8 'l," 1099

C3 .5 .40 13 C (834,8) 323.5 32. 33.5. . 243 26 C (4,014.0) 1126.5 1126.5 1126.5 112.

82 23 C (3,940.9) 1133.1 1133.1 1133.1 11 7 1 1133.133 27 C (4,485.1) 1250.5 1250.5 150.5 1255.5 1250.523 17 C 2,524.8) 758.7 758.7 758.7 756, 758. 787 13 I 1,515.4) 479.9 494.3 509.1 524.4 540.169 16 C (2,644.8) 794.8 794.8 794.8 794.8 794.837 15 C (2,418.4) 733.7 733.7 733.7 7.7 733.789 26 1 (18,203,8) 4663.2 4803.1 4947.2 5095.6 5248.5

97 17 1 (6,640.2) 1793 1846.8 1902.2 1959.3 2018.168 18 C (3,655.5) 1032.9 1032.9 1032.9 1032.9 1032.9

27 23 C (5,595.5) 1539.4 1539.4 1539.4 1539.4 1539.43 14 C (2,510.7) 728.3 728.3 728.3 728.3 728.315 23 C (7,247.1) 1950.4 1950.4 1950.4 1950.4 1950.484 13 C (2,577.7) 769.3 769.3 769.3 769.3 769.39 27 C (637.7) 264.7 264.7 264.7 264.7 264.7

99 24 1 (1,084.6) 378.6 390 401.7 413.8 426.230 27 C (10,589.6) 2792.4 2792.4 2792.4 2792.4 2792.4

85 19 C (5,552.8) 1507.5 1507.5 1507.5 1507.5 1507.510 21 C (9,842.2) 2607.6 2607.6 2607.6 2607.6 2607.6

95 23 1 (17,735.1) 4579.9 4717.3 4858.8 5004.6 5154.777 24 C (11,520.4) 2994.6 2994.6 2994.6 2994.6 2994.62 19 C (8,727.3) 2314.5 2314.5 2314.5 2314.5 2314.5

58 13 C (3,746.0) 1041.5 1041.5 1041.5 1041.5 1041.526 13 C (4,258.8) 1189.4 1189.4 1189.4 1189.4 1189.44 19 C (9,132.0) 2391.6 2391.6 2391.6 2391.6 2391.6

24 13 C (430.3) 209.3 209.3 209.Z 209,3 209.398 15 1 (17,940.9) 4604 4742.1 4884.4 5030,9 5181.87 11 C (3,080.0) 882.8 882.8 882.8 882.6 882.8

25 C (9,091.8) 2413.7 2413.7 2413.7 2413.7

79

SAMPLE SIMULATION OUTPUT

PROJECT SAVINGS SAYINGS SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS SAVINGSNUMBER YEAR t6 YEAR #7 YEAR #8 YEAR 19 YEAR 110 YEAR #II YEAR 112 YEAR #13

81 152.2 14. 152.2 152.218 189.7 189.7 189.7 189.7 189.7 189.7 189.7 189.794 184.3 189.8 195.5 201.4 207.4 207.4 207.4 207.492 270.3 278.4 286.8 295.4 304.3 304.3 304.3 304.3

61 624.5 624.5 624.5 624.5 624.5 624,5 624.5 624.538 688.1 688.1 688.1 688.1 688.1 688.1 688.1 688.190 529.1 545 561.4 578.2 595.5 595.5 595.5 595.553 1099.8 1099.8 1099.8 !099.8 1099,8 1099.8 1099.8 1099.840 323.5 323.5 323.5 32, 5 323.5 32.5 3.5.5. ... .12-7 32 , 5 33, L 32 3.

43 1126.5 1126.5 1126. 1126.5 1126.5 1126.5 1126.5 1126.582 1133.1 1133 . 11,1 11 1133 . 11.1 1133,1 11i313 1250.5 1250.5 1250.5 1250.5 125.5 1250.5 1250.5 125.5

758.7 758.7 758.7 758.7 758.7 758.7 758.7 758.,787 556.3 573 9.2 607.9 626.1 626.1 626.1 626,1

69 794,8 794.8 794.8 794.8 74.8 794.8 794.8 794.837 733.7 733.7 733.7 733.7 733.7 733.7 733.7 733.7

89 5406 5568.2 5735,2 5907.3 6084.5 6084.5 6084.5 6084.597 2078.6 2141 2205.2 2271.4 2j9,j 2339.5 2339.5 2339 .568 1032.9 1032.9 1032.9 1032.9 1032.9 1032.9 1032.9 1032.927 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4 1539.43 728.3 728.3 728,3 728.3 728.3 728.3 728.3 728. 3

15 1950.4 1950.4 1950.4 1950.4 1950.4 1950.4 1950.4 1950.484 769.3 769.3 769.3 769.3 769.3 769.3 769.3 769.39 264.7 264.7 264.7 264.7 264.7 264.7 264.7 264.7

99 439 452.2 465.8 479.8 494.2 494.2 494.2 494.230 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4 2792.485 1507.5 1507.5 1507.5 1507.5 1507.5 1507.5 1507.5 1507.510 2607.6 2607.6 2607.6 2607.6 2607.6 2607.6 2607.6 2607.695 5309.3 5468.6 5632.7 5801.7 5975.8 5975.8 5975.8 5975.877 2994.6 2994.6 2994.6 2994.6 2994.6 2994.6 2994.6 2994.62 2314.5 2314.5 2314.5 2314.5 2314.5 2314.5 2314.5 2314.5

58 1041.5 1041.5 1041.5 1041.5 1041.5 1041.5 1041.5 1041.526 1189.4 1189.4 1189.4 1189.4 1189.4 1189.4 1189,4 1189.44 2391.6 2391.6 2391.6 2391.6 2391.6 2391.6 2391.6 2391.6

24 209.3 209.3 209.3 209.3 209.3 209.3 209.3 209.398 5337.3 5497.4 5662.3 5832.2 6007.2 6007.2 6007.2 6007.27 882.8 882.8 882.8 882.8 882.8 882.8

57 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7

80

SAMPLE SIMULATION OUTPUT

PROJECT SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS SAVINSS SAVINGSNUMBER YEAR #14 YEAR #15 YEAR #16 YEAR #17 YEAR #18 YEAR 119 YEAR 120 YEAR 621

8118 189.7 189.7 189.7 189.7 189.7 189.7 189.7 189.7

94

92 304.3 304.3 304.3 304.3 304.3 304.361 624.5 624.5 624.5 624.5 624.5 624.5 624.5 624.5

38 688.1 688.1 688.1 688.1 688.1 688.1 688.1 688.1

9053 1099.8 1099.8 1099.8 1099.8 1099.8 1099.8 1099.8 1099.8

4043 1126.5 1126.5 1126.5 1126.5 1126.5 1126.5 1126.5 1126.582 1133.1 1133.1 1133.1 1133.1 1133.1 1133.1 1133.1 1133.133 1250.5 1250.5 1250.5 1250.5 1250.5 1250.5 1250.5 1250.5

23 758.7 758.7 758.7 758.7

8769 794.8 794.8 794.837 733.7 733.7

89 6084.5 6084.5 6084.5 6084.5 6084.5 6084.5 6084.5 6084.5

97 2339.5 2339.5 2339.5 2339.568 1032.9 1032.9 1032.9 1032.9 1032.9

27 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4 1539.4

3 728.315 1950.4 1950.4 1950.4 1950.4 1950.4 1950.4 1950.4 1950.4

849 264.7 264.7 264.7 264.7 264.7 264.7 264.7 264.7

99 494.2 494.2 494.2 494.2 494.2 494.2 494.2 494.2

30 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4

85 1507.5 1507.5 1507.5 1507.5 1507.5 1507.510 2607.6 2607.6 2607.6 2607.6 2607.6 2607.6 2607.6 2607.695 5975.8 5975.8 5975.8 5975.8 5975.8 5975.8 5975.8 5975.8

77 2994.6 2994.6 2994.6 2994.6 2994.6 2994.6 2994.6 2994.62 2314.5 2314.5 2314.5 2314.5 2314.5 2314.5

58

264 2391.6 2391.6 2391.6 2391.6 2391.6 2391.6

24

98 6007.2 6007.2

7

57 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7 2413.7

81

SAMPLE SIMULATION OUTPUT

MANPOWER SUM OFPROJECT SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS SAVINGS POSITIONSANNUALNUMBER YEAR #22 YEAR #23 YEAR #24 YEAR #25 YEAR #26 YEAR #27 SAVED SAVINGS NPV

81 10 1369.8 773.518 189.7 189.7 189.7 189.7 189.7 10 4932.2 152594 10 2444.4 1066.992 11 5411,9 1836.861 624.5 624.5 624.5 624.5 624.5 624.5 16 16861.5 385938 688.1 688.1 688.1 688.1 688.1 17 17890.6 4009.690 15 7018.8 2447.853 1099.8 1099.8 1099.8 1099.8 23 27495 6105.240 12 4205.5 1463.143 1126.5 1126.5 1126.5 1126.5 1126.5 23 29289 6305.882 1133.1 1133.1 23 26061.3 6124.733 1250.5 1250.5 1250.5 1250.5 1250.5 1250.5 25 33763.5 706623 18 12897.9 3561.287 15 7379.6 2368.369 18 12716.8 3573.537 18 11005.5 3162.289 6084.5 6084.5 6084.5 6084.5 6084.5 76 150810.8 32249.897 34 36931.6 10093.868 22 18592.2 4815.727 1539.4 1539.4 28 35406.2 8079.33 18 10196.2 2854.515 1950.4 1950.4 34 44859.2 10078.784 18 10000.9 2886.99 264.7 264.7 264.7 264.7 264.7 264.7 0 7146.9 1807.4

99 494.2 494.2 494.2 0 11260.1 2925.830 2792.4 2792.4 2792.4 2792.4 2792.4 2792.4 45 75394.8 15204.485 28 28642.5 7057.310 43 54759.6 12710.195 5975.8 5975.8 0 130188.8 30157.477 2994.6 2994.6 2994.6 48 71870.4 15385.32 39 43975.5 10633.3

58 22 13539.5 3652.126 24 15462.2 4189.94 40 45440.4 10873.5

24 0 2720.9 1056.498 75 82815.6 22531.47 20 9710.8 2653.8

57 2413.7 2413.7 2413.7 2413.7 0 60342.5 12817.5

82

SAMPLE SIMULATION OUTPUT

RANK RANK RANK TOTALPROJECT BY BY BY DoDNUMBER IRR ROI CPM IRR ROI CPM RANKING

81 147.7001 13.299 10.3 I 2 1 418 89.1001 23.178 21.28 2 1 2 594 7,.200Z 10.811 22.61 3 5 11

92 55.400% 12.189 40.364 4 3 4 1161 32.700Z 8.83 119.35 11 7 8 2638 30.000% 7.799 134.941 12 9 10 3190 38.200% 5.548 84.333 7 34 6 4753 28.300X 7.091 !68.596 19 14 19 5240 38.2001 5.038 69.567 8 40 5 5343 28.000% 7.297 174.522 23 12 23 5882 28.7061 6.613 i71.343) 18 20 22L. 60

33 27.800x 7.528 179.404 26 10 25 6123 29.700Z 5.108 140.267 14 37 12 6387 33.5001 4 .87 10 .. 027 10 46 7 6369 29.6001 4.808 146.933 1 47 14 76

37 29.700Z 4.551 134.356 13 54 9 7689 28.200x ,G.28 29. 524 21 8 48 7797 29.200 X 5.562 195.3 16 33 30 79

68 27.9001 5.086 166,159 24 38 18 8o27 27.4001 6,328 199.839 2 B 22 32 823 28.100i 4,061 139.483 22 60 11 93

15 26.8001 6.19 115 33 25 36 9484 28.7001 3.88 143.206 17 64 13 949 41.500h 11.207 100000 6 4 86 96

99 37.700Z 10.382 100000 9 6 81 9630 26.300Z 7.12 235.324 40 13 44 9785 26.900X 5.158 198.314 30 36 31 9710 26.3001 5.564 228.888 41 32 43 116

95 28.300X 7.341 100000 20 11 65 11677 25.9001 6.239 240.008 44 24 49 117

2 26.200% 5.039 223.777 42 39 41 122n

58 26.500% 3.614 170.273 36 68 50 12426 26.600% 3.631 177.45 34 67 24 1254 25.900% 4.976 228.3 43 41 42 126

24 A8.400X 6.323 100000 5 23 98 126

98 27.500X 4.616 239.212 27 53 47 1277 26.500% 3.153 154 38 76 16 13057 26.500% 6.637 100000 39 19 76 134

83

SAMPLE SIMULATION OUTPUT

BEGINNING TOTAL BEGINNING TOTALPROJECT BUDGET(DoD) NFV BUDGET (CARRY-OVER) NPVNUMBER $150,461.6 DoD $154,102.7 CARRY-OVER

8E 1558.6 15399.718 150145.8 153786,994 149919.7 153560.892 149475.7 153116.861 147566.1 151207.238 145272.1 148913.290 144007.1 147648.253 140129.4 143770.540 139294.6 142935.743 135280.6 138921.7

82 131339,7 134980.833 126854.6 130495.723 124329.8 127970.987 122814.4 126455.569 120169.6 123810.737 117751,2 121392,389 99547.4 103188.597 92907.2 96548.3

68 89251,7 92892.827 83656.2 87297.33 81145.5 84786.6

15 73898.4 77539.584 71320.7 74961.89 70683 74324.1

99 69598.4 73239.530 59008.8 62649.985 53456 57097.110 43613.8 47254.995 25878.7 29519.877 14358.3 17999.42 5631 9272.1

58 1885 225860.4 5526.1

26 1267.3 230050.34

24 1454.7 1056.498

226916.857

84

Appendix C: Annual Net Present Value Results

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

1 1 231,088.6 240,630.32 242,363.2 242,644.83 241,215.6 248,057.34 234,141.2 239,047.55 240,145.6 233,462.3

Total 1,188,954.2 1,203,842.2 -14,880.0

2 1 227,542.5 244,302.42 262,064.5 245,452.63 250,866.4 243,753.94 255,080.7 256,797.75 215,890.1 238,091.0

Total 1,211,444.2 1,228,397.6 -16,953.4

3 1 239,378.3 251,109.42 237,987.2 237,987.23 234,808.6 233,345.34 241,805.4 240,179.85 230,050.3 226,918.8

Total 1,184,029.8 1,189,538.5 -5,508.7

4 1 222,008.4 239,027.42 269,840.0 253,028.93 220,847.6 222,072.84 205,647.9 205,647.95 237,536.0 239,168.5

Total 1,155,879.9 1,158,945.5 -3,065.6

5 1 259,958.7 262,299.02 238,524.0 235,056.73 228,264.4 229,214.34 227,242.0 247,379.45 257,682.6 239,918.9

Total 1,211,671.7 1,213,888.3 2,196.6

85

ANNUAL NET PRESENT VALUE RESULTS

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

6 1 240,891.6 254,562.42 243,765.8 234,979.53 223,896.9 224,985.34 244,293.9 241,626.65 232,821.7 235,555.0

Total 1,185,689.9 1,191,708.8 6,038.9

7 1 226,382.7 227,560.12 227,007.2 231,793.73 224,526.1 226,297.64 222,061.1 228,432.45 254,209.1 244,403.5

Total 1,154,186.2 1,158,487.3 4,301.1

8 1 247,798.5 250,068.42 234,153.3 235,485.93 240,051.9 242,838.84 247,384.8 250,984.75 249,089.8 244,276.9

Total 1,218,478.3 1,223,654.7 5,176.4

9 1 223,300.5 224,336.22 216,881.6 218,343.53 261,328.1 266,120.74 245,279.5 242,088.15 236,043.5 248,098.4

Total 1,182,833.2 1,198,986.9 -16,153.7

10 1 234,702.9 237,683.92 232,057.6 232,752.73 238,452.2 233,059.84 242,780.5 239,001.95 240,532.9 244,427.6

Total 1,188,526.1 1,186,925.9 + 1,600.2

86

ANNUAL NET PRESENT VALUE RESULTS

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) (8 Thousand)

11 1 217,652.7 222,758.52 222,954 219,551.13 228,996.4 240,910.94 249,663.9 239,572.35 227,412.4 234,662.6

Total 1,146,679.4 1,157,455.4 -10,776

12 1 233,857.2 235,5702 227,151 227,1513 228,972.8 233,103.74 231,486.4 249,046.45 260,448.3 244,499.9

Total 1,181,915.7 1,189,371.0 -7,455.3

13 1 221,092.8 221,664.32 216,350.9 218,514.93 229,840.1 220,840.14 225,563.5 228,4325 239,120.7 240,089

Total 1,131,968.0 1,138,540.3 -6,572.3

14 1 203,825 213,284.52 241,281.8 229,669.23 246,563.6 238,824.94 229,606.2 235,384.35 252,612.1 250,959.0

Total 1,173,888.7 1,168,121.9 + 5,766.8

15 1 223,197 223,1972 221,028.6 232,675.43 246,351.3 236,328.74 232,175.5 227,794.05 218,837.3 224,065.6

Total 1,141,589.7 1,144,080.7 - 2,471

87

ANNUAL NET PRESENT VALUE RESULTS

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

16 1 229,881.1 237,204.12 243,720.8 238,135.73 233,302.2 233,302.24 233,337.0 238,436.85 253,364.8 245,902.7

Total 1,193,535.9 1,192,981.5 + 554.4

17 1 216,651.9 223,497.82 215,911.8 218,534.23 243,900.3 247,100.44 241,882.8 233,300.85 229,092.1 224,573.2

Total 1,147,438.9 1,147,006.4 + 432.5

18 1 213,530.7 226,087.82 248,254.7 243,400.53 236,694.6 232,663.54 245,737.9 240,970.55 209,662 217,258.8

Total 1,153,879.9 1,160,381.1 - 6,501.2

19 1 243,707.4 249,498.42 249,806.9 243,644.63 214,053.8 235,194.04 251,548.4 240,096.85 243,215.2 238,792

Total 1,202,328.9 1,207,225.8 4,896.9

20 1 259,945.5 260,772.92 214,949 220,7283 244,766.7 251,254.44 238,902.1 232,793.85 248,909 244,088.5

Total 1,207,472.3 1,209,567.6 2,095.3

88

ANNUAL NET PRESENT VALUE RESULTS

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

21 1 223,994.5 232,673.12 246,737.9 240,178.93 238,259.8 244,419.24 253,734 247,605.25 223,526.9 226,660.3

Total 1,186,253.1 1,191,536.7 5,283.6

22 1 224,840.5 226,936.22 216,165.8 226,779.53 268,086.4 255,269.84 244,292.6 251,014.45 251,620.9 245,429.7

Total 1,205,006,2 1,205,429.6 423.4

23 1 241,448 250,287.22 240,629.3 233,9953 235,225 237,357.94 231,143,7 234,165.35 243,348.5 239,546

Total 1,191,794.5 1,195,351.4 3,556.9

24 1 221,942.5 224,544.72 241,759.2 241,729.73 238,773.1 256,138.24 248,974.7 234,5655 235,188.3 229,581.7

Total 1,186,637.8 1,186,559.3 + 78.5

25 1 220,197.1 229,221.72 248,616.8 245,027.13 220,001.4 228,1234 244,521.2 241,809.45 235,709.1 235,709.1

Total 1,169,045.6 1,179,890.3 -10,844.7

69

ANNUAL NET PRESENT VALUE RESULTS

Run Year NPV NPV(Carry-over Method) (DoD Method) Difference

($ Thousand) ($ Thousand) ($ Thousand)

26 1 237,709 239,126.82 236,473.4 245,799.33 237,423.6 233,573.34 246,186.2 245,3035 231,455 235,106.7

Total 1,189,247.2 1,198,909.1 - 9,661.9

27 1 212,862.1 239,445.92 254,356.3 234,907.53 243,190 245,709.44 220,380.0 223,375.55 229,675.1 222,269.7

Total 1,160,464.3 1,165,708.0 5,243.7

28 1 216,890.2 224,701.72 227,048 224,705.33 230,600.7 225,093.44 234,663 239,025.55 249,851.7 247,339.1

Total 1,159,053.6 1,160,665.0 1,811.4

29 1 222,794.7 229,101.92 232,216.8 229,652.73 236,489.1 236,489.14 232,567.3 231,937.65 245,077.7 247,344.2

Total 1,169,145.6 1,174,524.6 5,37j

30 1 237,122.3 238,943.52 232,932.4 245,141.53 252,816.1 253,137.84 223,932.1 220,696.85 238,162.9 232,267.7

Total 1,184,965.8 1,190,187.3 5,221.5

90

Biblioaranhy

1. Christensen, David S. The APPlication of MathematicalProrammina to the Productivity Investment Fund Pronram;A Capital Rationing Problem. PhD dissertation.University of Nebraska, 1987 (AD-A186153).

2. Department of Defense Instruction 5010.36. ProductivityEnhancing Capital Investments. 31 December 1980.

3. Devore, Jay L. Probability and Statistics forEngineering and the Sciences (Second Edition). Monterey:Brooks/Cole Publishing Company, 1987.

4. Farragher, E. "Capital Budgeting Practices of Non-Industrial Firms," The Engineering Economist. 31:293-302 (Summer 1986).

5. Gobel, David P. Using Quattro. Carmel IN: QueTM

Corporation, 1988.

6. Gurnani, C. "Capital Budgeting: Theory and Practice,"The Engineerins Economist. 30: 19-46 (Fall 1984).

7. Kim, Suk H. and Edward J. Farragher. "Current CapitalBudgeting Practices," Management Accounting. 62: 26-30(June 1981).

8. Law, Averill M. and W. David Kelton. Simulation Modelinaand Analysis. New York: McGraw-Hill, Inc., 1982.

9. Para-Vasquez, A. and R. Oakford. "Simulation as aTechnique for Comparing Decision Procedures," TheEngineering Economist. 21: 221-236 (Summer 1976).

10. Quirin, G. David. The Capital Expenditure Decision.Homewood IL: Richard D. Irwin, Inc., 1967.

11. Scott, David F., Jr. and J. William Petty, II."Capital Budgeting Practices in Large American Firms:A Retrospective Analysis and Synthesis," The FinancialR itexw, 1.A: 111-123 (March 1984).

12. STATISTIX: An Interactive Statistical Analysis Prouramfor Microcomputers. Roseville MN: NH AnalyticalSoftware, undated.

13. Sundem, Gary L. "Evaluating Simplified Capital

Budgeting Models Using a Time-state Preference Metric,"Contem~orary Issues in Cost and Manaerial Accountina:A Discipline in Transition, edited by Hector R. Anton,Peter A. Firmin, and Hugh D. Grove. Boston: HoughtonMifflin, 1978.

91

14. Whitaker, David. "An Investigation into the DecisionRules of Capital Investment Using Simulation," Journalof the Operational Research Society. 35: 1101-1111,1984.

15. White, Bob E. Ranking Capital Investment Alternatives:A Computer Simulation. PhD dissertation. Iowa StateUniversity, Ames IA, 1980 (0N1342264).

16. Zimmerman, J. "Budgeting Uncertainty and the AllocationDecision in a Nonprofit Organization" Journl ofAccounting Research. 14: 301-319 (Autumn 1976).

92

Vi ta

Capt Albert F. Spala

S. .. He graduated from high school in St.

Louis, Missouri, in 1979 and attended Parks College of St.

Louis University in Cahokia, Illinois, from which he

received a Bachelor of Science degree in Aerospace

Engineering in December 1982. Upon graduation, he received

a commission in the USAF through the ROTC program. He

attended pilot training in May 1983 and was then assigned to

the Aeronautical Systems Division (ASD) at Wright-Patterson

AFB in Dayton, Ohio in August 1983. While at ASD, he served

as the Nuclear Warhead Integration Engineer on the Ground

Launched Cruise Missile program from August 1983 to June

1984. He then served as an Armament Integration Engineer on

the F-15E program where he became the F-15 Armament Chief

Systems Engineer in May 1987. He then entered the School of

Systems and Logistics, Air Force Institute of Technology, in

May 1988.-

93

.UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE

Form ApprovedREPORT DOCUMENTATION PAGE OMBNo. 0704-0188

la. REPORT SECURITY CLASSIFICATiON lb. RESTRICTIVE MARKINGS

UNCLASSIFIED2a. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORT

2b. DiCLASSIFICATION /DOWNGRADING SCHEDULE Approved for public release;distribution unlimited

4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S)

AFI T/GSM/LSY/89D- 386a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATIONSchool of Systems (If applicable)

and Logistics IAFIT/LSY6c. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City, State, and ZIP Code)

Air Force Institute of TechnologyWright-Patterson AFB OH 45433-6583

8a. NAME OF FUNDING/SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (If applicable)

8c. ADDRESS (City, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERSPROGRAM PROJECT TASK WORK UNITELEMENT NO. NO. N0_ ACCESSION NO.

11. TITLE (Include Security Classification)COMPARING RANKING HEURISTICS FOR THE PRODUCTIVITY INVESTMENT FUND PROGRAM:A CAPITAL RATIONING PROBLEM

12. PERSONAL AUTHOR(S)Albert F. Spala, B.S., Capt, USAF

13a. TYPE OF REPORT 113b. TIME COVERED 14. DATE OF REPORT (Year, Month,Oay) 15. PAGE COUNTMS Thesis I FROM TO _ 1989 September 7 105

16. SUPPLEMENTARY NOTATION

17. COSATj CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP Budgets Economic Analysis Money05 01' Capital Economic Models

19. ABSTRACT (Continue on reverse if necessary and identify by block number)

Thesis Advisor: David S. Christensen, Capt, USAFAssociate .ProfessorDepartment of Systems Acquisition Management

App d for blic rtease: IAW AFR 190-1.

RR 1. EMLHAINZ, LtCol USAF 12 Jan 90Director of Research and ConsultingAir Force Institute of Technology (AU)Wright-Patterson AFB OH 45433-6583

20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATIONE)UNCLASSIFIED/UNLIMITED I SAME AS RPT. 0 DTIC USERS UCLASSIFIED

22a. NAME OF RESPONSIBLE INDIVIDUAL 122b. TELEPHONE (Include Area Code) 22c. OFFICE SYMBOLDavi~d S. rChristennr. A q nC r rfeo=A =491_,' 2 I LSY,

DD Form 1473, JUN 86 Previous editions are obsolete. SECURITY CLASSIFICATION OF THIS PAGE

UNCLASSIFIED

UNCLASSIFIED

The purpose of this study was to compare two capitalrationing heuristics as they apply to the Department ofDefense (DoD) Productivity Investment Fund (PIF) program.Specifically, it addressed the research question: Is thenet present value (NPV) of capital investment projectsselected using the current DoD method less than the NPV ofprojects selected using an alternative Carry-over method ofproject selection?

The current DoD method of project selection allows theskipping of economically attractive projects to maximize theuse of an annual budget. The alternative Carry-over methodwould not allow skipping and would carry the funds remainingto the next annual budget without penalty. The largerbudget in the subsequent year could allow the funding of amore economically attractive project that might otherwise beskipped. The result may be more long term economic savingsto the DoD.

The study was performed using a QUATTRO personalcomputer spreadsheet simulation. Project characteristicswere generated based on FY85 PIF data and the process ofproject selection was performed over a five year period.Annual budgets were kept constant at $150 million (M) exceptfor the funds remaining from the previous years.

The study found that the five year total NPV of projectsselected using the current DoD method was greater than thealternative Carry-over method by an average of $5.135M.However, sensitivity analysis showed that by using excessprofitability index (EPI) as the only ranking criterion, thefive year NPV total of projects selected using the DODmethod of skipping could be increased by $63 M. The NPV ofprojects selected using the jarry-over method and the EPIcriterion also increased by an average of $64 M. The DoDmethod using the EPI" criterion was still- superior to theCarry-over method by an average of $4.234 M.

UNCLASSIFIED